Peck began his career as a child actor, appearing in the film Snow Day (2000) and the Nickelodeon sketch comedy series The Amanda Show (2000–2002).

Peck's film roles include Max Keeble's Big Move (2001), Spun (2002), Drillbit Taylor (2008), What Goes Up (2009), Red Dawn (2012), The Timber (2015), Chronically Metropolitan (2016), and Oppenheimer (2023).

Youth Theater and performed stand-up comedy at Carolines on Broadway for the Audrey Hepburn Foundation.

[13] At the age of 13, he was offered a role on Nickelodeon's The Amanda Show and, at his mother's suggestion, accepted the part and moved to Los Angeles to further pursue an acting career.

Peck made his film debut in Snow Day (2000), and appeared regularly on The Amanda Show until the end of its run in 2002.

[14] He also starred opposite Alex D. Linz and Zena Grey in the theatrical film, Max Keeble's Big Move, which was released on October 5, 2001.

During this period, Peck appeared in several independent films, including Spun and 2004's Mean Creek, for which he received critical praise.

He has also appeared in the series finale of What's New, Scooby-Doo?, an episode of Codename: Kids Next Door called "Operation: C.A.K.E.D.-F.I.V.E.

Peck played a high school bully in 2008's Drillbit Taylor, and starred in the films The Wackness (released July 2008), American Primitive, Safety Glass, and reprised his role as Eddie in Ice Age: Dawn of the Dinosaurs.

In 2011, Peck had a cameo role on the hit Nickelodeon show Victorious as an audience member for a play Jade wrote.

In 2012, Peck starred in the remake of Red Dawn, and once again reprised his role as Eddie, in Ice Age: Continental Drift.

In 2015, Peck was cast as a lead in the comedy series, Grandfathered, starring alongside John Stamos.

[17][18] Both Peck and Stamos are nominated for a 2016 People's Choice Award in the category "Favorite Actor In A New TV Series".

[29] In August 2021, Peck joined the cast of How I Met Your Father as Drew, an elementary school vice principal.

[41] In 2022, Peck revealed that he had struggled with addictions to alcohol and drugs in the past, stating, "I was always looking for something to fix my insides.

But eventually I realized that whether my life was beyond my wildest dreams or a total mess, it didn't change the temperature of what was going on in my mind.