Of course it is a drug. All medicines are drugs.
And if you meant to ask "Is birth control a psychoactive drug?" the answer would also be yes. It messes with a woman's hormones, which obviously affects her psychologically. Many stories of women's personality changing completely after starting birth control.
Not to mention, they legally refer to hormonal birth control as a "contraceptive" when it is really an abortaficent. In other words, fertilization takes place, and then the fertilized embryo is flushed out of the body. They get away with legally calling it a "contraceptive" because it prevents implantation of the fertilized embryo in the uterus. If it never makes it to the uterus, it is not legally considered a "pregnancy" (although conception did occur, and the embryo was killed). This is very misleading, if you ask me. There are lots of women who wrongly believe that birth control prevents conception, and would not use it if they knew the truth. Even if you're pro-abortion or whatever, you should still support women being told the truth in order to make informed decisions, and not deliberately misled by the pharmaceutical companies in order to sell more pills.