  We study B^+/- --> J/psi pi^+/- and B^+/- --> J/psi K^+/- decays in a sample
of about 89 million BB~ pairs collected with the BABAR detector at the PEP-II
asymmetric B-factory at SLAC. We observe a signal of 244 +/- 20 B^+/- --> J/psi
pi^+/- events and determine the ratio BF(B^+/- --> J/psi pi^+/-)/BF(B^+/- -->
J/psi K^+/-) to be [5.37 +/- 0.45 (stat.) +/- 0.11 (syst)]%. The charge
asymmetries for the B^+/- --> J/psi pi^+/- and B^+/- --> J/psi K^+/- decays are
determined to be A_pi = 0.123 +/- 0.085 (stat.) +/- 0.004 (syst.) and A_K =
0.030 +/- 0.015 (stat.) +/- 0.006 (syst.), respectively.
