The FBI investigates crimes and, when the evidence warrants, makes a recommendation to the Justice Department. It is up to Justice to bring an indictment.
This is no different from local law enforcement. The police don't issue indictments. They present evidence to local prosecutors. The city, county, or state prosecutors bring the indictment.
Separation of powers and all that.
Question: Can the F.B.I. Director hold a public news conference in which he states there is overwhelming evidence of criminal wrongdoing on Hillary's part, and therefore he strongly recommends that the Justice Department indict her? Even if the Justice Department declined to follow through on the recommendation, the damage to Hillary's campaign from the resulting media frenzy would be enormous.