ANOVA for 5-likert scale comparing 3-4 groups?

I have to compare the answers of 3 or 4 different groups (this depends on each question). The questions asked are asking the participants to fill in a 5-likert scale (totally disagree, disagree, not disagree nor agree, agree and totally agree).

Can I use ANOVA for this? And how do I do this in R?

My recommendation is to use ordered logistic regression or some other model from Item response theory. In R you can use polr function from MASS package (here is a nice tutorial) or use MCMC samplers such as rSTAN or rJAGS for more flexibility.