Yes you can. Factor analysis for binary items is called item response theory (IRT) or latent trait models. For the relationships between different factor analytic models depending on whether the observed items are binary or not, see Bartholomew et al (https://www.wiley.com/en-us/Latent+Variable+Models+and+Factor+Analysis%3A+A+Unified+Approach%2C+3rd+Edition-p-9780470971925), among other sources.