In this paper, we propose a Bayesian approach for affine auto-calibration. By the Bayesian approach, a posterior distribution for the affine camera parameters can be constructed, where also the prior knowledge can be taken into account. Moreover, due to the linearity of the affine camera model, the structure and translations can be analytically marginalised out from the posterior distribution, if certain prior distributions are assumed. The marginalisation reduces the dimensionality of the problem substantially that makes the MCMC methods better suitable for exploring the posterior of the intrinsic camera parameters. The experiments verify that the proposed approach is a versatile, statistically sound alternative for the existing affine auto-calibration methods.