We compute the partial capture rate of negative muons in³He by following the analysis of Peterson to include the relativistic corrections and the exchange effects, for various values of theg_p/g_A ratio. We also calculate the total capture rate. The ground state of³He is assumed to be spherical. The radial dependence of the ground state wave function is taken to be (a) one parameter Irving function, (b) a modified three-parameter Irving function and (c) a function having ‘soft-core’, whose parameters have been fixed in a variational calculation of the binding energy of the triton using a non-local momentum-dependent potential involvingp² terms. The calculated values of the capture rates are compared with the experimental data to find a value for theg_p/g_A ratio.