This paper considers applying Physical-layer Network Coding (PNC) to OFDM modulated Mobile Ad-hoc Networks (MANETs) to resolve the outstanding issue of short contact time between nodes due to their mobility. Ideally, PNC enables data exchange twice faster than traditional scheduling and thus, it is a potential performance booster in MANETs. However, application of PNC in MANETs is challenged by the carrier frequency offset (CFO) problem inherently caused by nodemotion induced Doppler shifts and asynchronous oscillators. CFO induces inter-carrier interference (ICI) that degrades PNC performance. In this paper, we investigate the CFO/ICI impact on the signal-to-interference-and-noise ratio (SINR) and bit error rate (BER) in the signal detection of PNC in a two-way relay channel (TWRC) based on BPSK modulation. We find that PNC with power control suffers at most 3 dB SINR penalty compared with generic point-to-point communications in both the flat fading and the frequency-selective channels. Also, we find that a belief propagation (BP) algorithm could be employed in the signal detection of PNC to effectively tackle ICI and reduce its impact on the BER of PNC. For CFO compensation in PNC, we propose a method that amounts to positioning the relay's local oscillator frequency at the middle of the received frequencies from the two end nodes in the TWRC. Importantly, we show that (i) this compensation method can theoretically maximize the worst SINR in PNC; and (ii) in case of similar CFO of the two uplinks in TWRC, it allows PNC to achieve a BER at the relay close to that in the ideal case, i.e., in point-to-point communications without CFO. Overall, this paper demonstrates that mobile PNC is feasible in general, laying the foundation for future studies.