We present ultraviolet , optical , and near-infrared observations of SN 2012ap , a broad-lined Type Ic supernova in the galaxy NGC 1729 that produced a relativistic and rapidly decelerating outflow without a gamma-ray burst signature . Photometry and spectroscopy follow the flux evolution from -13 to +272 days past the B -band maximum of -17.4 \pm 0.5 mag . The spectra are dominated by Fe ii , O i , and Ca ii absorption lines at ejecta velocities of v \approx 20,000 km s ^ { -1 } that change slowly over time . Other spectral absorption lines are consistent with contributions from photospheric He i , and hydrogen may also be present at higher velocities ( v \gtrsim 27,000 km s ^ { -1 } ) . We use these observations to estimate explosion properties and derive a total ejecta mass of \sim 2.7 { M } _ { \odot } , a kinetic energy of \sim 1.0 \times 10 ^ { 52 } erg , and a ^ { 56 } Ni mass of 0.1 - 0.2 { M } { { } _ { \odot } } . Nebular spectra ( t > 200 d ) exhibit an asymmetric double-peaked [ O i ] \lambda \lambda 6300 , 6364 emission profile that we associate with absorption in the supernova interior , although toroidal ejecta geometry is an alternative explanation . SN 2012ap joins SN 2009bb as another exceptional supernova that shows evidence for a central engine ( e.g. , black-hole accretion or magnetar ) capable of launching a non-negligible portion of ejecta to relativistic velocities without a coincident gamma-ray burst detection . Defining attributes of their progenitor systems may be related to notable properties including above-average environmental metallicities of Z \gtrsim { Z } _ { \odot } , moderate to high levels of host-galaxy extinction ( E ( B - V ) > 0.4 mag ) , detection of high-velocity helium at early epochs , and a high relative flux ratio of [ Ca ii ] / [ O i ] > 1 at nebular epochs . These events support the notion that jet activity at various energy scales may be present in a wide range of supernovae .