A McDonald's Big Mac is displayed on a page of the McDonald's app.

McDonald's digital app for deals and promotions is gaining traction with consumers, according to Jefferies.

The firm reiterated its buy rating on McDonald's shares, citing optimism over the restaurant chain's remodeling efforts.

Same-store sales should benefit from the app as well as the fast food company's efforts to revamp its restaurants. The mobile app is driving customers to promotions like $1 drinks, $1 sandwiches and free fries with a $1 purchase. "We also see deeper penetration as customers take advantage of value offers," analyst Andy Barish said in a note to clients Tuesday, estimating gains in same-store sales of 3 percent.

There are also more mentions of special McDonald's menu items on social media, something that is also seen driving sales and average check size. "Mentions of Big Macs (in association with the 50th Anniversary promotion) and fresh beef (quarter-pounders and Signature Crafted) are up noticeably," Barish said.

McDonald's shares closed up less than 1 percent on Tuesday.

Barish reaffirmed his $190 price target for McDonald's shares, representing 18 percent upside to Monday's closing price.

The analyst cited SimilarWeb data, which revealed that average daily active users on McDonald's Android app rose by 20 percent to 40 percent in recent months.

"MCD app downloads and install penetration data suggest digital strategy working," he said in the note.

McDonald's shares are underperforming the market this year. The stock is down 7 percent year to date through Monday versus the S&P 500's 8 percent gain.