In this work, we investigate the capacity of a block fading one-bit multi-antenna channel without a priori channel state information. We consider the asymptotic regime with a large number of receive antennas. We show that the capacity scales as ${1\over2}{\binom{T}{2}} \log (\alpha_{snr,T} n_r)$ under the peak power constraint and with coherence block size T. In particular, we derive the exact form of $\alpha_{snr,T}$ for T=2 and T=3. Furthermore, for an arbitrary value of T, we derive a lower bound of $\alpha_{snr,T}$ by proposing low-complexity signaling scheme. We also obtain a closed-form expression of $\alpha_{snr,T}$ when the SNR is small.