The spin-lattice relaxation time, $T_1$, for $^{69}Ga$, $^{71}Ga$, and $^{75}As$ nuclei in GaAs:$Mn^{2+}$ single crystals was measured as a function of temperature. The values of $T_1$ for $^{69}Ga$, $^{71}Ga$, and $^{75}As$ nuclei were found to decrease with increasing temperature. The $T_1$ values in GaAs:$Mn^{2+}$ crystal are similar to those in pure GaAs crystal. The calculated activation energies for the $^{69}Ga$, $^{71}Ga$, and $^{75}As$ nuclei are 4.34, 4.07, and 3.99 kJ/mol. It turns out that the paramagnetic impurity effect of $Mn^{2+}$ ion doped in GaAs single crystal was not strong on the spin-lattice relaxation time.