It is difficult to pinpoint exactly what year this novel is set in, though we get enough clues to make an educated guess. We can see from the copyright page that the book received its copyright in 1986, and many of the textual clues would seem to confirm this as the approximate timing: computers are used but clearly not as frequently as they came to be used by the end of the 1990s and early 2000s, for example.
We also know that each handmaid term, so to speak, lasts two years, and that this is Offred's third Commander. There was, in addition, a training period at the Rachael and Leah Center before she was assigned to her first household, and so it stands to reason that the present of the story takes place some seven years, give or take, after the creation of the Republic of Gilead.
Offred also refers to "one of the first [churches] erected here," in what used to be the United States of America, "hundreds of years ago." This would have been sometime in the mid- to late-seventeeth century, so it stands to reason that the timing is the late twentieth-century, given this reference as well as the ones to televisions, computers, and cars. We can reasonably assume, then, that the text takes place sometime in the 1980s or 1990s. The fact that Offred records her tale on cassette tapes, which we learn in the Historical Notes, also points to this period.