The Shooter, the 1997 movie which features Randy Travis as Kyle Tapert, is now streaming on Amazon Prime.
I think this movie must have changed its name at some point because some places, including on Amazon, show it as Deadly Shooter, while other places show it as The Shooter.
Film synopsis from Amazon:
When a fearless gunslinger rides into the sleepy town of Kingston, all the locals seem to want a piece of him. Some praise him for his heroism; some envy his high-caliber sharpshooting. Others want to see him six feet under. He stops to save a damsel in distress and is thrust onto a treacherous path lined with psychotic outlaws, corrupt lawmen and bandits out for revenge.