Scott Eastwood is starving. On a recent afternoon, the 29-year-old heartthrob barrels into a conference room at Twentieth Century Fox after a morning of press for his new movie, “The Longest Ride,” where he plays a bull-wrangling cowboy. He eyes the lunch buffet, unwrapping tinfoil and stacking two plates with chicken, fish and vegetables, a potluck for one. Then he sits down and realizes he might need to devour this meal with his bare hands. “I don’t have a fork,” says Eastwood, the son of screen legend Clint. “I don’t know what’s going on here.” A publicist rushes over with silverware. “Ah, ah, woo-hoo! You got some forks for us,” Eastwood says.

Even though he’s acted for 12 years, mostly in smaller roles, Eastwood’s career is now on the upswing. Eastwood has just arrived in New York from Hawaii, where he plays a NSA agent in the upcoming Oliver Stone drama about Edward Snowden. Then he’ll jet to Toronto for an unspecified part in David Ayer’s “Suicide Squad.” Eastwood has read the script, but he’s not able to divulge any details about the comic book tentpole, where he’s rumored to play Wonder Woman’s boyfriend Steve Trevor. “It’s going to be something that no one has seen before,” he says. “It’s so f—ing cool.”

But he’s happy to chat about “The Longest Ride” — which opens in theaters on Friday — his first lead role in a movie. “I’m really proud of it,” he says. The tearjerker about a cowboy who falls in love with a local Southern girl (Britt Robertson) is adapted from a Nicholas Sparks novel, and could provide the same launching pad for Eastwood that “The Notebook” was for Ryan Gosling. Besides, Hollywood is experiencing a shortage of leading men, and Eastwood — with his strong screen presence (which he learned from his dad, who told him: “Don’t be afraid of doing nothing”) and pinup looks — fits the job description.

When asked about the kind of career he envisions for himself, Eastwood rolls through a list of A-listers that include his pal Leonardo DiCaprio, Mark Wahlberg, Brad Pitt, George Clooney and Matt Damon. But his performance in “The Longest Ride” also brings to mind another young movie star on the verge of stardom — Channing Tatum in “Step Up.” “I think he will continue on this path,” says “Longest Ride” director George Tillman Jr.

Eastwood would have missed out on “The Longest Ride” if he’d landed a coveted part he auditioned for around the same time — as Chris Kyle’s brother in “American Sniper.” But the director of that film, who happens to be his dad, never contacted him after he submitted a tape. “I’ve auditioned for pretty much every one of my father’s movies,” says Eastwood, who appeared in “Flags of Our Father,” “Invictus” and “Gran Torino” (but got shot down for “J. Edgar”). For the movies where he’s not picked, he doesn’t even receive a gentle rejection letter. “You don’t get a phone call,” Eastwood says. “It’s nothing personal.”

When he was growing up in Monterey, Calif., where he discovered acting in high school, Eastwood was so conscious about not benefiting from nepotism, he took on his mom’s last name — as Scott Reeves. But he’s come to embrace the Eastwood brand. He was one of five leading men that Tillman Jr. saw for the part of Luke Collins. “When he came in, I thought it was his dad 25 years ago,” the director says. “He looked exactly like him. I said, ‘This isn’t going to work. People are going to think it’s Clint Eastwood in the movie.’” But Eastwood won him over after a chemistry test with his leading lady.

Despite his early film work, Eastwood was mostly anonymous until he appeared in a Town & Country cover shoot (baring his abs and biceps) in October 2013 that went viral. “For some reason, people made a big deal out of it, but I don’t see it,” Eastwood says. “There are a lot more in-shape guys, better-looking guys, than me.” Shortly after, he was in the running to play Christian Grey in “Fifty Shades of Grey” after Charlie Hunnam dropped out. But Eastwood refused to audition because Universal Pictures wouldn’t let him see the script first. “They wanted me to sign a deal before I went in and even tested for it, which to me is backwards,” Eastwood says. “I thought it could make a good movie. The problem is, if you don’t have a script, you don’t know what movie they are going to make.”

Even if he didn’t enter the Red Room, the Internet is swooning over his pictures on Instagram — where he’s often seen shirtless in San Diego. “I’m not trying to post shirtless photos,” Eastwood says. “The reality is, I’m from California, where it’s f—ing hot. I live by the beach. I’m at the beach all the time. I surf. I fish. I dive. These things on Instagram are really my life with my buddies doing my normal day-to-day stuff. I happen to be shirtless a lot.”

“The Longest Ride” benefits from his sex appeal. Eastwood appears sans shirt (and pants) in a love scene in the shower with Robertson. Tillman Jr. says that he wanted to make the scene racier than a typical Sparks movie, but ultimately had to tone down some of the footage — including nudity from Robertson — to land a PG-13 rating. The director made sure one important moment didn’t end up on the cutting room floor. “We kept Scott’s butt shot in the film,” Tillman Jr. says. “The test audience didn’t want to lose that.”

To play the part, Eastwood had to learn how to come across as a cowboy (his dad hasn’t seen the film yet). A stunt double was used for the bull-riding scenes, but Eastwood had to get on and off, which turned out to be a dangerous exercise. “You’re surrounded by metal,” Eastwood says. “There’s a 2,000 pound bull underneath your legs. It can buck up at any second with its horns.” After the three-month shoot in North Carolina wrapped, Eastwood convinced his stunt double to let him ride, ignoring the studio’s instructions not to do that. “They told me, ‘We need you to promote a movie and be alive,’” Eastwood says. He survived — for 2.5 seconds. But his time in Hollywood is sure to be a much longer ride.