Wireless neural recording technologies are severely constrained by the limited energy efficiencies and telemetry bandwidth, while data compression or feature extraction techniques can be utilized to relax the burdens on the wireless data link. Compressed Sensing (CS) is an emerging approach for efficient data compression in wireless sensing applications. However, state-of-the-art CS encoder designs still lead to large area and energy overheads. This paper presents a novel CS encoder hardware design by incorporating deterministic measurement matrix, namely Quasi-Cyclic Array Code (QCAC) matrix, to improve overall area and power metrics over prior arts, while still preserving comparable signal recovery performance based on classic reconstruction algorithms. We demonstrate the advantages of the proposed QCAC-CS encoder design for spike data compression in neural recording application. Compared to the state-of-the-art CS encoder designs, QCAC-based CS encoder achieves on average (with compression ratio ranging from 0.0625 to 0.25) 42.7% and 49.5% reduction in encoder area and total power consumption, respectively. And the compressed spikes from the QCAC-CS encoder can be recovered with comparable performance toward random matrix based CS encoder designs.