He played college football for the Oklahoma Sooners and was selected by the Los Angeles Chargers in the first round of the 2020 NFL draft.

Murray announced that he would forgo his senior season to declare for the 2020 NFL draft.

[7] Murray was selected by the Los Angeles Chargers with the 23rd pick in the 2020 NFL Draft.

In Week 13 against the Patriots, Murray led the team with 14 tackles (12 solo) and recorded his first career sack on Cam Newton during the 45–0 loss.

[14] On April 28, 2023, the Chargers opted to decline the fifth-year option of Murray's contract, making him a free agent in 2024.