We present a novel method for rapidly acquiring optical coherence tomography (OCT) images at multiple backscattering angles. By angularly compounding these images, high levels of speckle reduction were achieved. Signal-to-noise ratio (SNR) improvements of 3.4 dB were obtained from a homogeneous tissue phantom, which was in good agreement with the predictions of a statistical model of speckle that incorporated the optical parameters of the imaging system. In addition, the fast acquisition rate of the system (10 kHz A-line repetition rate) allowed angular compounding to be performed in vivo without significant motion artifacts. Speckle-reduced OCT images of human dermis show greatly improved delineation of tissue microstructure.