Written and first recorded by Tony Joe White (1972).
Also recorded by Billy Lee Riley (1972).
Hit version by Elvis Presley (US #39/C&W #4/MOR #27/UK #33 1974).
From the wiki: “‘I’ve Got a Thing About You Baby’ is a soulful, laid-back track written and first recorded in 1972 by Tony Joe White, a singer-songwriter known for his swamp rock style. The song was first released in 1972 on White’s album The Train I’m On. It has a bluesy, groove-heavy vibe with a subtle romantic charm, which fits well within White’s signature style that blends country, blues, and rock.