Speckle noise significantly limits the information content provided by coherent optical imaging methods such as optical coherence tomography and its recent derivative, optical frequency-domain imaging (OFDI). In this paper, we demonstrate a novel OFDI system that simultaneously acquires hundreds of angularly resolved images, which can be compounded to reduce speckle noise. The system comprises an InGaAs line-scan camera and an interferometer, configured so that the elements of the detector array simultaneously capture light spanning a backscattering angular range of 32 degrees. On successive read-outs of the array, the wavelength of the laser source was stepped through a range of 130 nm centered at 1295 nm to concurrently generate 400 angle-resolved OFDI images. A theory of angle-resolved OFDI and the design equations of the system are presented. Incoherent averaging of the angle-resolved data is shown to yield substantial speckle reduction (as high as an 8 dB SNR improvement) in images of a tissue phantom and esophageal tissue ex vivo.