Can you get worms by having sexual intercourse with someone?

Yes: Yes, sexual intercourse can get many sexually transmitted bacterias and virus, such as herpes, syphilis, hiv, gonorrhea, chlamydia, and papillomavirus.

Worms?: Yes, there is potential exposure to pinworms, strongyloides, and several other parasites. Some of these will depend on whether you are engaging in activities along with intercourse, such as oral sex, analingus, anal intercourse, and so on.