Raman spectroscopy (RS) and optical coherence tomography (OCT) are powerful tools for optical analysis of tissues with mutually complementary strengths and limitations. OCT excels at visualizing tissue microstructure but lacks molecular specificity, while RS can relay tissue biochemical composition but typically cannot relate microstructure. Previous implementations of combined RS-OCT have utilized a common sample arm while maintaining independent RS and OCT detection arms. We present the design and application of an integrated RS-OCT instrument with a common detection arm for both RS and OCT. The detector is a spectrograph capable of sequential detection of the 855-nm OCT signal and the Raman scatter generated by a 785-nm source. The capabilities of the instrument are demonstrated ex vivo in the calvaria and retina of rodents, as well as in vivo in human skin.