Asomugha's first onscreen role was on The CW sitcom The Game, followed by roles in other television series, including Friday Night Lights and the TNT drama Leverage. He also appeared in Will Ferrell's comedy web series Funny or Die (2012) and the Roadside Attractions film Hello, My Name Is Doris (2015).
In 2014, Asomugha worked as an executive producer on the Netflix film Beasts of No Nation. The film premiered at the 72nd Venice International Film Festival and was a critical success, garnering numerous awards that year, including a nomination for Best Feature at the 2016 Film Independent Spirit Awards.
Asomugha's breakout performance came when he produced and starred in the Amazon Studios film Crown Heights. The film premiered in competition in the US Dramatic Category at the Sundance Film Festival on January 23, 2017, where it received favorable reviews and won the Audience Award for U.S. Dramatic Film. Following its success, Asomugha was widely regarded as one of the breakout actors of the 2017 Sundance Film Festival, with Jenelle Riley of Variety calling his performance "simply astounding." He was later nominated for Best Supporting Actor at the 2018 Film Independent Spirit Awards, as well as Outstanding Supporting Actor in a Motion Picture at the NAACP Image Awards.
Asomugha made his stage debut in the Off-Broadway play Good Grief (2018) at the Vineyard Theatre. The play was named a New York Times Critic's Pick, and Sara Holdren of New York Magazine praised Asomugha's performance as "excellent."
Asomugha has served as a producer or executive producer on several film and theatre projects, including the Focus Features film Harriet (2019), the Apple Studios film The Banker (2020), and the Amazon Studios film Nanny (2022), which won the Grand Jury Prize at the 2022 Sundance Film Festival. He has also produced for theatre, including the Broadway plays American Son (2018) and Purlie Victorious (2023), which was nominated for the Tony Award for Best Revival of a Play.
In 2020, Asomugha received critical acclaim for his Broadway debut in the Pulitzer Prize-winning play A Soldier's Play, portraying Private First Class Melvin Peterson, a role originally performed off-Broadway by Denzel Washington. Jesse Green of The New York Times praised his standout performance as "excellent," while David Rooney of The Hollywood Reporter declared it a "promising Broadway debut." The production went on to receive seven Tony Award nominations, winning Best Revival of a Play.
Also in 2020, Asomugha produced and starred alongside Tessa Thompson in the Amazon Studios romantic drama Sylvie's Love. Both Asomugha and the film received high praise from critics after premiering at the 2020 Sundance Film Festival. In his review, Vince Mancini of Uproxx wrote, "It's a rare wonder to find out that an ex-athlete is both an actor and a great actor at the same time." Benjamin Lee of The Guardian praised the chemistry between Thompson and Asomugha, calling it "a genuine, pulse-quickening connection that's impossible to feign and rare to witness." Asomugha went on to receive an NAACP Image Award nomination for Outstanding Actor in a Television Movie, Limited Series, or Dramatic Special. The following year, he earned his first Primetime Emmy Award nomination as a producer when Sylvie's Love was nominated for Outstanding Television Movie.
In 2022, Asomugha starred opposite Eddie Redmayne and Jessica Chastain in the Netflix thriller The Good Nurse. The film premiered at the Toronto International Film Festival to generally favorable reviews. On February 2, 2024, Deadline announced that Asomugha and Chastain would reunite on the Apple TV+ thriller miniseries The Savant, inspired by the true story of a top-secret investigator who infiltrates online hate groups.
On January 18, 2022, Deadline announced that Asomugha would make his directorial debut with the feature film The Knife, from a script he co-wrote with Mark Duplass. In addition to directing, he would also star alongside Academy Award-winning actress Melissa Leo, Aja Naomi King, and Manny Jacinto. The film premiered in competition at the Tribeca Film Festival on June 9, 2024, receiving high critical praise and rave reviews. Many critics cited it as a "remarkable and powerful directing debut," while also lauding the "strong and poignant performances" from the ensemble cast. Film critic Will Bjarnar, in his review for Next Best Picture, said that "the film was as engaging a work of suspense as I've seen this year." Lovia Gyarkye, a critic for The Hollywood Reporter, highlighted the film's "chilling and visceral frankness," calling it "not just a story of horror, but of heartbreak."
Asomugha won the Tribeca Film Festival Award for Best New Narrative Director, and The Knife was nominated for the Founders Award for Best U.S. Narrative Feature. The film had its European premiere on September 11, 2024, at the Deauville American Film Festival, where it won the Jury Prize and was nominated for the festival's Grand Prix.
On November 4, 2024, Asomugha was honored with the Breakthrough Director Award at the Denver Film Festival.