We present a technique for estimating the optical thickness of subvisual cirrus clouds detected by OSIRIS (Optical Spectrograph and Infrared Imaging System), a limb-viewing satellite instrument that measures scattered radiances from the UV to the near-IR. The measurement set is composed of a ratio of limb radiance profiles at two wavelengths that indicates the presence of cloud-scattering regions. Cross-sections and phase functions from an in situ database are used to simulate scattering by cloud-particles. With appropriate configurations discussed in this paper, the SASKTRAN successive-orders of scatter radiative transfer model is able to simulate accurately the in-cloud radiances from OSIRIS. Configured in this way, the model is used with a multiplicative algebraic reconstruction technique (MART) to retrieve the cloud extinction profile for an assumed effective cloud particle size. The sensitivity of these retrievals to key auxiliary model parameters is shown, and it is shown that the retrieved extinction profile, for an assumed effective cloud particle size, models well the measured in-cloud radiances from OSIRIS. The greatest sensitivity of the retrieved optical thickness is to the effective cloud particle size. Since OSIRIS has an 11-yr record of subvisual cirrus cloud detections, the work described in this manuscript provides a very useful method for providing a long-term global record of the properties of these clouds.