Well, while the origin of the game of carrom itself might be obscure, the origin of this uncertainty is certainly thanks to our great American cousins, who prefer to simply spell words "conveniently" !
The answer to this simple question is the same as that to "Colour or Color ?", "Jewellery or Jewelry", "Cheque or Check ?" and many more. Thankfully, most dictionaries do acknowledge this fact, and show the two spellings as variants of each other.
Nevertheless, "Carrom" is certainly the well accepted international spelling for the game, as adopted by the International Carrom Federation as well.
Interestingly enough, the number of results found for the search term "carom" are almost one and a half times that for the politically correct "carrom" on the leading search engine Google.