Four variants are listed in the apparatus of the 3rd corrected edition of the Greek New Testament (UBS3) in 1 Cor 13. 3. They are:
κανχήσωμαı (P A B 048 pc)
κανθήσωμαı (K ψ majority text)
κανθήσομαı (C D F G L pc)
κανθήσεταı (1877 2492 pc)
Of these variants κανθσομαı seems to be the most popular, occurring in texts such as the 2nd edition of the British and Foreign Bible Societies, Vogels, Kilpatrick's Diglot, Von Soden, Tischendorf's 9th edition and the 25th edition of Nestle-Aland. It is also favoured by Elliott, De Boor, Grosheide, Godet, Morris, Bachmann, Billerbeck, Wolff, Weiss, Robertson and Plummer, Pop, Groenewald, Lietzmann, Barrett and Kieffer. Κανθήσωμαı seems to be the second most popular reading, occurring in amongst others the Textus Receptus, Alford, The Greek New Testament according to the Majority Text, Souter and Scrivener.