Photoacoustic computed tomography (PACT), a fast-developing modality for deep tissue imaging, images the spatial distribution of optical absorption. PACT usually treats the absorption coefficient as a scalar. However, the absorption coefficients of many biological tissues exhibit an anisotropic property, known as dichroism or diattenuation, which depends on molecular conformation and structural alignment. Here, we present a novel imaging method called dichroism-sensitive PACT (DS-PACT), which measures both the amplitude of tissue's dichroism and the orientation of the optic axis of uniaxial dichroic tissue. By modulating the polarization of linearly polarized light and measuring the alternating signals through lock-in detection, DS-PACT can boost dichroic signals from biological tissues. To validate the proposed approach, we experimentally demonstrated the performance of DS-PACT by imaging plastic polarizers and ex vivo bovine tendons deep inside scattering media. We successfully detected the orientation of the optic axis of uniaxial dichroic materials, even at a depth of 4.5 transport mean free paths. We anticipate that the proposed method will extend the capability of PACT to imaging tissue absorption anisotropy.