Catalyzes the exchange of L-carnitine for gamma-butyrobetaine. (R)-carnitine(out) + 4-(trimethylamino)butanoate(in) = (R)-carnitine(in) + 4-(trimethylamino)butanoate(out) kcat is 263 min(-1) with L-carnitine as substrate (PubMed:20829798). kcat is 4.9 sec(-1) with L-carnitine as substrate (PubMed:24101465). Optimum pH is 7. Amine and polyamine metabolism; carnitine metabolism. Homotrimer. Belongs to the BCCT transporter (TC 2.A.15) family. CaiT subfamily.