Spin currents can exert spin-transfer torques on magnetic systems even in the limit of vanishingly small net magnetization, as is the case for antiferromagnets. Here, we experimentally show that a spin-transfer torque is operative in a material with weak, short-range magnetic order -- namely, a macroscopic ensemble of superparamagnetic-like Co nanomagnets. We employ element- and time-resolved X-ray ferromagnetic resonance (XFMR) spectroscopy to directly detect sub-ns dynamics of the Co nanomagnets, excited into precession with cone angle $geq$0.003$^{circ}$ by an oscillating spin current. XFMR measurements reveal that as the net moment of the ensemble decreases, the strength of the spin-transfer torque increases relative to those of magnetic field torques. Our findings point to spin-transfer torque as an effective way to manipulate the state of nanomagnet ensembles at sub-ns timescales.