We describe an alkali-metal magnetometer for detection of weak magnetic fields in the radio-frequency (rf) range. High sensitivity is achieved by tuning the Zeeman resonance of alkali atoms to the rf frequency and partially suppressing spin-exchange collisions in the alkali-metal vapor. We demonstrate magnetic field sensitivity of 2 fT/Hz(1/2) at a frequency of 99 kHz with a resonance width of 400 Hz. We also derive a simple analytic expression for the fundamental limit on the sensitivity of the rf magnetometer and show that a sensitivity of about 0.01 fT/Hz(1/2) can be achieved in a practical system with a measurement volume of 200 cm3.