Yes, taking the sum could be one approach. However, if your sample is sufficiently large, you have many options. If you search for structural equation modeling (SEM) with categorical variables, you should find the best practices you are looking for (e.g., [check this tutorial][1]; also see Edwards, Wirth, & Houts 2012, and Cai 2013).

**References**

Cai, L. (2013). Factor analysis of tests and items.

Edwards, M. C., Wirth, R. J., Houts, C. R., & Xi, N. (2012). Categorical data in the structural equation modeling framework.


  [1]: https://personality-project.org/r/tutorials/summerschool.14/rosseel_sem_cat.pdf