You could add the presumed moderator as covariate in ANCOVA,I have run a two-way between groups ANOVA to analyse my data. However, I have one more variable, which is not one of the factors in the ANOVA. I want to see how this variable interacts with one of the factors. I predicted that it will be a moderator.

and also the moderator*factor interaction.

Yes, that is very common.Other way is to run a regression and add this variable as a predictor, and the product of the interaction with the other IV.

With kind regards

K.