Yes, it is possible. In fact, the turkey baster method for IUI is one of the oldest methods to carry out an artificial insemination at home. The turkey baster is used as the tool for inserting the semen sample into the vagina.
It is useful because it transfers the sperm as close to the area of fertilization as possible. However, nowadays we can find safer tools for DIY artificial insemination, such as syringes.
Some sperm banks around the world include a syringe when you buy a semen sample for at-home insemination. They are used exactly the same as turkey basters, but with the advantage that they are easier to use.