STIs & STDs are caused by viruses or bacteria that like warm, soft, moist places such as your mouth and genital area (penis, vulva, vagina, anus, area between penis and anus, and area between vulva and anus). STIs can spread from the genital area to the mouth and from the mouth to the genital area. They are generally passed between people via body fluids or direct contact with skin or sores.
Though there's admittedly less risk of STIs in oral sex than in vaginal or anal sex, the risk still exists. You can get a bacterial infection of Chlamydia, syphilis, or gonorrhea (all of which can be passed from an infected mother to her baby during vaginal childbirth) in your mouth and/or throat, and in some rarer occasions, can develop genital warts in the mouth. Herpes (e.g. cold sores) is commonly passed between genitals and the mouth, and HIV can be passed through cuts in the mouth or small abrasions.
So yes, it can happen.