Cirrus clouds are important modulators of the Earth radiation budget and continue to be one of the most uncertain components in weather and climate modeling. Sun photometers are widely accepted as one of the most accurate platforms for measuring clear sky aerosol optical depth (AOD). However, interpretation of their measurements is ambiguous in the presence of cirrus. Derivation of a valid AOD under cirrus conditions was focused previously on correction factors, rather than on derivation of cirrus cloud optical thickness (COT). In the present work, we propose a new approach that uses the total measured irradiance to derive cirrus COT and ice particle effective diameter (Deff). For this approach, we generate lookup tables (LUTs) of total transmittance for the Sun photometer field of view (FOV) due to the direct and scattered irradiance over the spectral range of 400~2200 nm, for a range of cirrus COT (0~4), and a range of ice cloud effective diameters (10~120 mm) by using explicit cirrus optical property models for (a) cirrus only and (b) a two-component model including cirrus and aerosols. The new approach is tested on two cases (airborne and ground-based) using measured transmittances from the 14-channel NASA Ames Airborne Tracking Sun photometer. We find that relative uncertainties in COT are much smaller than those for Deff. This study shows that for optically thin cirrus cases (COT < 1.0), the aerosol layer between the instrument and the cloud plays an important role, especially in derivation of Deff. Additionally, the choice of the cirrus model may introduce large differences in derived Deff.