The standard electrocardiogram (ECG) is a point-wise evaluation of the body potential at certain given locations. These locations are subject to uncertainty and may vary from patient to patient or even for a single patient. In this work, we estimate the uncertainty in the ECG induced by uncertain electrode positions when the ECG is derived from the bidomain model. In order to avoid the high computational cost associated to the solution of the bidomain model in the entire torso, we propose a low-rank approach to solve the uncertainty quantification problem. More precisely, we exploit the sparsity of the ECG and the lead field theory to translate it into a set of deterministic, time-independent problems, whose solution is eventually used to evaluate expectation and covariance of the ECG. We assess the approach with numerical experiments in a simple geometry.