This paper proposes a probabilistic inverse consistency image registration network using a sparse BNN for cardiac motion estimation, aiming to simultaneously measure aleatoric and epistemic uncertainty. We construct a sparse BNN to predict the distribution parameters of the inverse consistency transformations between two images. Two symmetric Variational Autoencoders (VAEs) are constructed to predict the distribution parameters of latent variables in deformation space. The posterior distribution parameters of network weights are estimated during optimization, and only important weights are updated. Our sparse BNNs significantly reduce the computational cost and improve the registration accuracy by Bayesian model averaging (BMA). Experiments on a public cardiac MR dataset show that our sparse BNNs significantly improve the accuracy of the bidirectional registration for small datasets. It also provides aleatoric and epistemic uncertainty of registration results.