Direct-conversion radio transceivers can offer reprogrammable and low-cost hardware solutions for full-duplex (FD) cognitive radio (CR) devices. However, they are susceptible to radio frequency (RF) impairments, such as in-phase (I) and quadrature (Q) imbalance (IQI), which can significantly constrain the spectrum sensing capabilities. This paper is devoted to quantify and evaluate the effects of IQI in the context of spectrum sensing in FD CR systems, in which self-interference suppression (SIS) techniques are employed. Specifically, closed-form expressions are derived for the false alarm and detection probabilities, under three different scenarios: imperfect SIS with joint transmitter (TX) and receiver (RX) IQI, imperfect SIS and ideal TX/RX RF front-end, and perfect SIS and ideal TX/RX RF front-end. The derived analytical results are validated through extensive simulations, which reveal that IQI has a detrimental impact on the spectrum sensing performance of the FD CR transceiver, which brings significant losses in the spectrum utilization.