No, fertility treatments are carried out at a fertility clinic or medical facility. In the case of AI, it can be done at the gynecologist's office, due to the simplicity of the technique. Conversely, special equipment is required for all of the IVF steps involved to be carried out properly.
There is, however, an alternative to artificial insemination which is known as at-home artificial insemination. It is mainly a do-it-yourself version of AI in which the woman can get herself inseminated with donor or partner sperm by just buying an insemination kit at the pharmacy.
It should be taken into account that its chances of success are exactly the same as those you would achieve through natural conception. Besides, it involves a series of health risks, as the equipment has not been previously sterilized and therefore the risk of introducing germs into the vaginal tract is higher.