He worked as an attorney-adviser in the U.S. Department of Justice's Office of Legal Counsel from 2006 to 2008, as part of President George W. Bush's administration.

[3] In 2015, Oldham wrote an amicus curiae brief in support of Abbott's successful challenge of President Barack Obama's Deferred Action for Childhood Arrivals executive order.

[6] Abbott appointed Oldham as general counsel to replace Jimmy Blacklock, who left to take a seat on the Supreme Court of Texas.

[9] On February 12, 2018, President Donald Trump announced his intent to nominate Oldham to an undetermined seat on the United States Court of Appeals for the Fifth Circuit.

President Trump nominated Oldham to the seat vacated by Judge Edward C. Prado, who became the United States Ambassador to Argentina.

[14] In September 2022, Oldham wrote for a unanimous three-judge panel of the Fifth Circuit in NetChoice v. Paxton, which concerned the constitutionality of Texas House Bill 20.

In May 2024, Oldham wrote an opinion for a unanimous three-judge panel of the Fifth Circuit in Hughes v. Garcia, which affirmed the denial of qualified immunity to two Houston police officers who arrested a Good Samaritan for impersonating a police officer after he performed a citizen's arrest on a drunk driver who crashed in front of him while on a highway.