Moehrig attended Smithson Valley High School in Spring Branch, Texas, just north of San Antonio, where he played cornerback and receiver for the Rangers in addition to running track.

[2] As a true freshman at TCU in 2018, Moehrig transitioned to safety and made an immediate impact, starting two games on defense and being named the Horned Frogs' Special Teams MVP for the season.

[13] Defensive coordinator Gus Bradley selected Moehrig and Johnathan Abram to be the starting safety tandem to begin the regular season.

[14] On September 13, 2021, Moehrig earned his first career start in his professional regular season debut and recorded five combined tackles (three solo) in a 33–27 victory against the Baltimore Ravens.

He completed his rookie season in 2021 with a total of 55 combined tackles (36 solo), six pass deflections, and an interception in 17 games and 17 starts and was subsequently named to the PFWA NFL All-Rookie Team.

[20] Moehrig entered training camp slated to retain his role as the starting free safety under new defensive coordinator Patrick Graham.

In Week 14, Moehrig made eight combined tackles (five solo), a career-high three pass deflections, recovered a fumble, and was credited with half a sack in a 13–28 loss at the Tampa Bay Buccaneers.

He completed the 2024 NFL season with 104 combined tackles (64 solo), ten pass deflections, two interceptions, two fumble recoveries, and one sack while he started all 17 games.