Cognitive radio (CR) networks face significant challenges in spectrum sensing, especially under spectrum scarcity. Fluid antenna systems (FAS) can offer an unorthodox solution due to their ability to dynamically adjust antenna positions for improved channel gain. In this letter, we study a FAS-driven CR setup where a secondary user (SU) adjusts the positions of fluid antennas to detect signals from the primary user (PU). We aim to maximize the detection probability under the constraints of the false alarm probability and the received beamforming of the SU. To address this problem, we first derive a closed-form expression for the optimal detection threshold and reformulate the problem to find its solution. Then an alternating optimization (AO) scheme is proposed to decompose the problem into several sub-problems, addressing both the received beamforming and the antenna positions at the SU. The beamforming subproblem is addressed using a closed-form solution, while the fluid antenna positions are solved by successive convex approximation (SCA). Simulation results reveal that the proposed algorithm provides significant improvements over traditional fixed-position antenna (FPA) schemes in terms of spectrum sensing performance.