We present a search for anisotropic cosmic birefringence in 500 \deg ^ { 2 } of southern sky observed at 150 GHz with the SPTpol camera on the South Pole Telescope . We reconstruct a map of cosmic polarization rotation anisotropies using higher-order correlations between the observed cosmic microwave background ( CMB ) E and B fields . We then measure the angular power spectrum of this map , which is found to be consistent with zero . The non-detection is translated into an upper limit on the amplitude of the scale-invariant cosmic rotation power spectrum , L ( L + 1 ) C _ { L } ^ { \alpha \alpha } / 2 \pi < 0.10 \times 10 ^ { -4 } rad ^ { 2 } ( 0.033 \deg ^ { 2 } , 95 % C.L . ) . This upper limit can be used to place constraints on the strength of primordial magnetic fields , B _ { 1 Mpc } < 17 { nG } ( 95 % C.L . ) , and on the coupling constant of the Chern-Simons electromagnetic term g _ { a \gamma } < 4.0 \times 10 ^ { -2 } / H _ { I } ( 95 % C.L . ) , where H _ { I } is the inflationary Hubble scale . For the first time , we also cross-correlate the CMB temperature fluctuations with the reconstructed rotation angle map , a signal expected to be non-vanishing in certain theoretical scenarios , and find no detectable signal . We perform a suite of systematics and consistency checks and find no evidence for contamination .