Manziel currently plays in the state with the Texas A&M Aggies, where he has built up a reputation as one of the brightest prospects in college football.
The 21-year-old won the prestigious Heisman Trophy in 2012 and has been affectionately nicknamed 'Johnny Football' by fans.
Tony Buzbee is one such fan, and he is desperate to see Manziel continue playing in the state, commissioning the billboard, which reads "Keep Johnny football in Texas!" and directs people to a website supporting the cause.
That website contains an edited image of Manziel wearing the Texans top as well as a petition imploring Texans owner Bob McNair to pick the quarterback.
"This site is dedicated to supporting Johnny Manziel as the No. 1 draft pick of the Houston Texans in 2014," reads a note on the site.
"To win in the NFL, a team must have a quarterback with strong leadership skills, a winning attitude and lots of talent. Johnny Manziel is a winner and he is a unique talent. College football has never seen anything like him."
The Texans lost the last 14 games of the 2013 season to end the campaign with a 2-14 record.