We study gated field-effect transistors (FETs) with an eccentric Corbino-disk geometry, such that the drain spans its circumference while the off-center inner ring acts as a source. An alternating current terahertz potential difference is applied between source and gate while a static source-drain voltage, rectified by the nonlinearities of FET electrons, is measured. When a magnetic field is applied perpendicular to the device, a strong resonance appears at the cyclotron frequency. The strength of the resonance can be tuned by changing the eccentricity of the disk. We show that there is an optimum value of the eccentricity that maximizes the responsivity of the FET.