Cooper pairs in superconductors are normally spin singlet. Nevertheless, recent studies suggest that spin-triplet Cooper pairs can be created at carefully engineered superconductor-ferromagnet interfaces. If Cooper pairs are spin-polarized they would transport not only charge but also a net spin component, but without dissipation, and therefore minimize the heating effects associated with spintronic devices. Although it is now established that triplet supercurrents exist, their most interesting property - spin - is only inferred indirectly from transport measurements. In conventional spintronics, it is well known that spin currents generate spin-transfer torques that alter magnetization dynamics and switch magnetic moments. The observation of similar effects due to spin-triplet supercurrents would not only confirm the net spin of triplet pairs but also pave the way for applications of superconducting spintronics. Here, we present a possible evidence for spin-transfer torques induced by triplet supercurrents in superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions. Below the superconducting transition temperature T_c, the ferromagnetic resonance (FMR) field at X-band (~ 9.0 GHz) shifts rapidly to a lower field with decreasing temperature due to the spin-transfer torques induced by triplet supercurrents. In contrast, this phenomenon is absent in ferromagnet/superconductor (F/S) bilayers and superconductor/insulator/ferromagnet/superconductor (S/I/F/S) multilayers where no supercurrents pass through the ferromagnetic layer. These experimental observations are discussed with theoretical predictions for ferromagnetic Josephson junctions with precessing magnetization.