We study the sum-rate capacity of the Z-interference channel with a relay (Z-ICR) in the weak interference regime, when the channel coefficients are subject to phase fading. This fading model represents many practical communication systems in which phase noise is a major concern, such as OFDM communications and line-of-sight microwave communications. We consider the case in which the relay receives transmissions from only one of the two transmitters, but the transmission of the relay is received at both destinations. We present conditions on the channel coefficients under which the sum-rate capacity of the phase fading Z-ICR is achieved by treating interference as noise at each receiver, and derive the corresponding sum-rate capacity. Our results show the benefits of relaying in the presence of interference when interference is weak and relay power is finite.