Mediates the electroneutral exchange of acylcarnitines (O-acyl-(R)-carnitine or L-acylcarnitine) of different acyl chain lengths (ranging from O-acetyl-(R)-carnitine to long-chain O-acyl-(R)-carnitines) with free carnitine ((R)-carnitine or L-carnitine) across the mitochondrial inner membrane, via a ping-pong mechanism. Key player in the mitochondrial oxidation pathway, it translocates the fatty acids in the form of acylcarnitines into the mitochondrial matrix, where the carnitine palmitoyltransferase 2 (CPT-2) activates them to undergo fatty acid beta-oxidation. Catalyzes the unidirectional transport (uniport) of carnitine at lower rates than the antiport (exchange). (R)-carnitine(out) + O-acetyl-(R)-carnitine(in) = (R)-carnitine(in) + O-acetyl-(R)-carnitine(out) (R)-carnitine(out) + O-acyl-(R)-carnitine(in) = (R)-carnitine(in) + O-acyl-(R)-carnitine(out) (R)-carnitine(out) + O-propanoyl-(R)-carnitine(in) = (R)-carnitine(in) + O-propanoyl-(R)-carnitine(out) (R)-carnitine(out) + O-hexadecanoyl-(R)-carnitine(in) = (R)-carnitine(in) + O-hexadecanoyl-(R)-carnitine(out) (R)-carnitine(out) + O-octanoyl-(R)-carnitine(in) = (R)-carnitine(in) + O-octanoyl-(R)-carnitine(out) (R)-carnitine(in) = (R)-carnitine(out) Belongs to the mitochondrial carrier (TC 2.A.29) family.