In this paper, the performance of short constraint length convolutional codes in imperfect phase tracking conditions is discussed. Convolutional codes are used to provide error protection to a particular user in an Asynchronous CDMA (A- CDMA) system undergoing slow Rician fading. Maximum likelihood decoding with a Viterbi algorithm recovers the information symbols. A Phase Locked Loop (PLL) depicting the variations in the phase error for abrupt phase changes in the input signal is considered. Analytical bounds, which are useful in predicting the performance of the A-CDMA system are derived and plotted for the cases of infinite and finite channel memory. The upper bounds on the unconditional Bit Error Rate (BER) with Viterbi decoding are derived and plotted for the various convolutional codes considered. The simulated BERs are found to agree well with their upper bounds.