The call came to Austin Droogsma’s cell phone in late April, and he was certain he was being punked or scammed.

“Austin, this is Charles Tisch with the New York Giants,’’ the call began. “We want you to come up and try out at rookie minicamp.’’

“My first response was like, ‘You know I didn’t play football in college, right?’ ’’ a disbelieving Droogsma told Tisch, a football operations assistant with the Giants. “He said, ‘Oh yeah, we know.’ I was like, ‘OK, well now that we got that out of the way,’ that they didn’t think I was somebody else.’’

Droogsma didn’t play a down of football in his four years at Florida State. He was a shot-putter on the track and field team with Tokyo 2020 Olympic aspirations. The last time Droogsma wore a helmet and pads was in the fall of 2012 while playing at Gulf Breeze High School in the Florida Panhandle.

“I didn’t really think it was real,’’ Droogsma said. “I thought somebody was messing with me. I thought it was some kind of scam.’’

It was not a scam. It was real.

Droogsma was one of 10 players invited to the Giants’ rookie tryout on May 3. The percentage of undrafted tryout invitees who make it to the next level — training camp — is not high. But Droogsma impressed the coaches enough to land a three-year, $1.7555 million contract, the standard minimum rookie deal.

Now, wearing No. 66 in Giants blue, he’s vying for at least a spot on the practice squad and a new career he never dared to dream about.

“It’s pretty crazy,’’ Droogsma said. “I definitely didn’t see it coming at all.’’

This whole thing has moved rather rapidly for Droogsma, who had been making ends meet working as a security guard.

“It definitely took a couple days for me after that call for it to sink in,” he said, “because I was still thinking, ‘What is going on? This is not real life.’ ”

Then it dawned on Droogsma that he had eight days to relearn how to play football, so he called his friend Landon Dickerson, who had been a guard on the Florida State football team and just transferred to Alabama.

“I was like, ‘Dude, you’re not going to believe this, but I just got a call from the freaking New York Giants and they want me to come up to rookie minicamp,’ ’’ Droogsma told Dickerson. “He was like, ‘What?’ And I’m like, ‘Yeah, I know.’ I said, ‘Can you help me train?’ ’’

Droogsma said he “started literally from ground zero.’’

“We started with me getting into a stance,’’ he said. “I know the stance that I was going to get in and the stance that he put me in were two completely different things.’’

Just three-plus months after Droogsma’s “ground zero’’ training with Dickerson, starting center Jon Halapio said he believes it’s possible Droogsma’s dream has a chance to continue beyond these dog days of training camp.

“Since Austin’s been here, he’s accepted every challenge that’s been thrown his way,’’ Halapio told The Post on Saturday. “He’s actually doing better than I thought he was going to do coming from track and not playing football.’’

Halapio said the possibility of Droogsma sticking with the practice squad is “realistic for him, because since he’s been here, I’ve seen growth in him and I’ve seen his awareness in the game. Whether it’s blocking twists or blitzes, I see him starting to react to those things. Once you see growth in a player like that you know he’s trending the right way.

“If he’s whiffing on blocks play after play, then maybe you’re worried about a guy not knowing what he’s doing.’’

Offensive line coach Hal Hunter said the 6-foot-3, 331-pound Droogsma is “coming along quickly’’ and added, “You’re starting with a blank tape, which is sometimes easier than a tape you have to erase” because of poor habits.

“He’s developed,’’ head coach Pat Shurmur said. “It’s fair to say since he hasn’t played football in a very long time and to then try to do it at this level is a big challenge. We’ll just have to see where it goes.’’

Wherever it goes, Droogsma is playing with house money.

“The way I look at it is I have nothing to lose,’’ Droogsma said. “I either gain a lot or I go right back to what I was doing. If I go right back to what I was doing, at least I have this super-awesome story that I can tell people.’’

He said making the practice squad “is a realistic goal.’’

“I don’t see myself beating out anybody anytime soon,’’ Droogsma said. “I don’t think being on the final 53 [-man roster] is realistic until next year … and that’s if they keep me around.’’

Droogsma said East Rutherford is the furthest north he ever has traveled. He also never has attended an NFL game.

“My first NFL game could be as a player,” he said. “It’s really crazy to think I am in a position that some of these guys have worked their entire lives for.”