Active reconfigurable intelligent surface (A-RIS) aided integrated sensing and communications (ISAC) system has been considered as a promising paradigm to improve spectrum efficiency. However, massive energy-hungry radio frequency (RF) chains hinder its large-scale deployment. To address this issue, an A-RIS-aided ISAC system with antenna selection (AS) is proposed in this work, where a target is sensed while multiple communication users are served with specifically selected antennas. Specifically, a cuckoo search-based scheme is first utilized to select the antennas associated with high-gain channels. Subsequently, with the properly selected antennas, the weighted sum-rate (WSR) of the system is optimized under the condition of radar probing power level, power budget for the A-RIS and transmitter. To solve the highly non-convex optimization problem, we develop an efficient algorithm based on weighted minimum mean square error (WMMSE) and fractional programming (FP). Simulation results show that the proposed AS scheme and the algorithm are effective, which reduce the number of RF chains without significant performance degradation.