Daily_wanderer, I see that your button identification request is your very first post at Treasure Net. So, welcome to T-Net's "What Is It?" forum... the best place on the internet to get unknown objects CORRECTLY identified.
Your button's ID:
As others have already (correctly) said, it is a Confederate Infantry "Script I" button for an enlisted-man's uniform. (Enlisted-men's ranks were Private, Corporal, and Sergeant... meaning, the non-officer ranks.)
More specifically... although relic-diggers call the type of letter on you button a "Script I" -- the button-collector reference books say it is actually an Old English letter I.
Your button was manufactured in Britain, most probably by the firm of Smith. Kemp, & Wright of Birmingham England, specifically for export to the Confederacy. That being said...the majority of these "Script I" buttons have a backmark saying 'S. Isaacs Campbell & Company / 71 Jermyn St London" -- which was the name of the Export business company in Britain created by Confederate Government agents to purchase and export military supplies. You say you found it in North Texas. Therefore, it most likely entered Texas on a Blockade-runner ship in the harbor at Galveston Texas.