| Year | Award | Category | Nominated work | Result | Ref. |
| 2010 | Alliance of Women Film Journalists | Best Ensemble Cast | The Social Network | Nominated | |
| Hollywood Film Festival Awards | Ensemble of the Year | Won | |
| Toronto Film Critics Association Awards | Best Supporting Actor | Won | |
| Chicago Film Critics Association Awards | Most Promising Performer | Nominated | |
| Phoenix Film Critics Society Awards | Best Ensemble Acting | Won | |
| San Diego Film Critics Society Awards | Best Ensemble Performance | Nominated | |
| Southeastern Film Critics Association Awards | Best Ensemble | Won | |
| Village Voice Film Poll | Best Supporting Actor | 8th place | |
| Washington D.C. Area Film Critics Association Award | Best Ensemble | Nominated | |
| 2011 | Central Ohio Film Critics Association | Best Ensemble | Nominated | |
| Critics' Choice Awards | Best Acting Ensemble | Nominated | |
| Palm Springs International Film Festival | Ensemble Cast Award | Won | |
| Screen Actors Guild Awards | Outstanding Performance by a Cast in a Motion Picture | Nominated | |
| Teen Choice Awards | Choice Movie Breakout: Male | Nominated | |
| Young Hollywood Awards | Male Star of Tomorrow | — | Won | |
| Dallas–Fort Worth Film Critics Association Awards | Best Supporting Actor | J. Edgar | 4th place | |
| Houston Film Critics Society Award | Best Supporting Actor | Nominated | |
| 2012 | Screen Actors Guild Awards | Outstanding Performance by a Male Actor in a Supporting Role | Nominated | |
| 2013 | CinemaCon | Male Star of Tomorrow | — | Won | |
| Teen Choice Awards | Choice Movie: Chemistry (shared with Johnny Depp) | The Lone Ranger | Nominated | |
| 2016 | San Diego Film Critics Society Awards | Best Ensemble | Nocturnal Animals | Nominated | |
| 2017 | Central Ohio Film Critics Association | Best Ensemble | Nominated | |
| Austin Film Critics Association | Best Supporting Actor | Call Me by Your Name | Nominated | |
| Chicago Film Critics Association | Best Supporting Actor | Nominated | |
| Dallas–Fort Worth Film Critics Association | Best Supporting Actor | 4th place | |
| Dublin Film Critics' Circle | Best Actor | 6th place | |
| Florida Film Critics Circle | Best Supporting Actor | Nominated | |
| IndieWire Critics Poll | Best Supporting Actor | 3rd place | |
| Online Film Critics Society | Best Supporting Actor | Nominated | |
| Phoenix Critics Circle | Best Supporting Actor | Nominated | |
| San Francisco Film Critics Circle | Best Supporting Actor | Nominated | |
| Seattle Film Critics Society | Best Ensemble Cast | Nominated | |
| Washington D.C. Area Film Critics Association | Best Supporting Actor | Nominated | |
| Vancouver Film Critics Circle Awards | Best Supporting Actor | Nominated | |
| 2018 | AACTA Award | Best Supporting Actor | Nominated | |
| Chlotrudis Awards | Best Performance by an Ensemble Cast | Nominated | |
| Critics' Choice Award | Best Supporting Actor | Nominated | |
| Denver Film Critics Society | Best Supporting Actor | Nominated | |
| Dorian Awards | Supporting Film Performance of the Year — Actor | Nominated | |
| Empire Award | Best Actor | Nominated | |
| Golden Globe Award | Best Supporting Actor – Motion Picture | Nominated | |
| Independent Spirit Award | Best Supporting Male | Nominated | |
| Iowa Film Critics Association | Best Supporting Actor | Nominated | |
| Satellite Award | Best Supporting Actor | Nominated | |
| Village Voice Film Poll | Best Supporting Performance | 12th place | |
| Texas Film Hall of Fame | One to Acclaim Award | — | Won | |
| SCAD Savannah Film Festival | Outstanding Achievement in Cinema | Call Me by Your Name, Sorry to Bother You, Hotel Mumbai, and On the Basis of Sex | Won | |
| 2019 | Shorty Awards | Storyteller of the Year | — | Nominated | |
| Broadway.com Audience Awards | Favorite Breakthrough Performance (Male) | Straight White Men | Nominated | |