Basal ganglia are usually attributed a role in facilitating willed action, which is found to be impaired in Parkinson's disease, a pathology of basal ganglia. We hypothesize that basal ganglia possess the machinery to amplify will signals, presumably weak, by stochastic resonance. Recently we proposed a computational model of Parkinsonian reaching, in which the contributions from basal ganglia aid the motor cortex in learning to reach. The model was cast in reinforcement learning framework. We now show that the above basal ganglia computational model has all the ingredients of stochastic resonance process. In the proposed computational model, we consider the problem of moving an arm from a rest position to a target position: the two positions correspond to two extrema of the value function. A single kick (a half-wave of sinusoid, of sufficiently low amplitude) given to the system in resting position, succeeds in taking the system to the target position, with high probability, only at a critical noise level. But for suboptimal noise levels, the model arm's movements resemble Parkinsonian movement symptoms like akinetic rigidity (low noise) and dyskinesias (high noise).