"excellent, fine, good, valuable," 1560s, from rome "fine" (1560s), said to be from Romany rom "male, husband" (see Romany). E.g. rum kicks "Breeches of gold or silver brocade, or richly laced with gold or silver" [Grose, "Dictionary of the Vulgar Tongue," 1785].
A very common 16c. cant word, by 1774 it also had come to mean "odd, strange, bad, spurious," perhaps because it had been so often used approvingly by rogues in reference to one another. This was the main sense after c. 1800.