Spin-phonon coupling mediated by single ion anisotropy was investigated using optical spectroscopy and first-principles calculations in the all-in-all-out pyrochlore magnet Cd_{2}Os_{2}O_{7}. Clear anomalies were observed in both the phonon frequencies and linewidths at the magnetic ordering temperature. The renormalization of the phonon modes was exceptionally large, signifying the presence of an unconventional magnetoelastic term from large spin-orbit coupling. In addition, the relative phonon frequency shifts show a strong correlation with the modulation of noncubic crystal field by the corresponding lattice distortion. Our observation establishes a new type of spin-phonon coupling through single ion anisotropy, a second-order spin-orbit coupling term, in Cd_{2}Os_{2}O_{7}.