We investigate the localization of random copolymers using the model of Garel [Europhys. Lett. 8, 9 (1989)], with the incorporation of excluded volume effects, based on a trial potential approach. Analytic solutions are produced for the case of evenly distributed randomness. Scaling behavior is predicted from numerical solutions for the case of uneven randomness. We find a critical temperature associated with monomer size, and a logarithmic increase in localization dimension near this transition.