In this paper, we consider the problem of polar coding for block fading channels without any instantaneous channel state information (CSI). We first decompose a block fading channel of T c symbols per coherent interval into T c binary-input sub-channels in a mutual-information-preserving way, and then design a multilevel (MLC) polar coding scheme for them. The proposed scheme achieves the ergodic mutual information of binary-input block fading channels with only channel distribution information (CDI). Simulations results are presented to compare the performance of the proposed MLC scheme and polar codes designed for i.i. d. fading channels with interleaving, which can provide some guidance for practical designs.