Radio frequency (RF) magnetometers based on nitrogen vacancy centers in diamond are predicted to offer femtotesla sensitivity, but previous experiments were limited to the picotesla level. We demonstrate a femtotesla RF magnetometer using a diamond membrane inserted between ferrite flux concentrators. The device provides ~300-fold amplitude enhancement for RF magnetic fields from 70 kHz to 3.6 MHz, and the sensitivity reaches ~70 fT√s at 0.35 MHz. The sensor detected the 3.6-MHz nuclear quadrupole resonance (NQR) of room-temperature sodium nitrite powder. The sensor's recovery time after an RF pulse is ~35 μs, limited by the excitation coil's ring-down time. The sodium-nitrite NQR frequency shifts with temperature as -1.00±0.02 kHz/K, the magnetization dephasing time is T2*=887±51 μs, and multipulse sequences extend the signal lifetime to 332±23 ms, all consistent with coil-based studies. Our results expand the sensitivity frontier of diamond magnetometers to the femtotesla range, with potential applications in security, medical imaging, and materials science.