We designed and fabricated an arrayed-waveguide grating (AWG) in silicon oxynitride as a spectrometer for spectral domain optical coherence tomography (SD-OCT). The AWG has a footprint of only $3.0\mathrm{cm}\times 2.5\mathrm{cm}$ , operates at a center wavelength of $1300\mathrm{nm}$ , and has $78\mathrm{nm}$ free spectral range. OCT measurements are performed that demonstrate imaging up to a maximum depth of $1\mathrm{mm}$ with an axial resolution of $19\mathrm{\mu m}$ , both in agreement with the AWG design parameters. Using the AWG spectrometer combined with a fiber-based SD-OCT system, we demonstrate cross- sectional OCT imaging of a multilayered scattering phantom.