If you’re being investigated for committing rape, you have all the same rights and protections that any criminal accused has. This includes the right to avoid self-incrimination (often called the “right to remain silent” or “Miranda right”), the right to be protected from unreasonable (which usually means warrantless) searches, and also the Sixth Amendment right to confront witness against you. This means that yes, you—or rather your lawyer; you should not try to defend yourself from a rape charge, but rather should retain legal counsel to represent you—can put your accuser on the stand and cross examine her.
In many states, what are known as “rape shield laws” will limit your ability to question her about her sexual background or history (if you had been intending to do that), but you can certainly question her about the her statements, accusations, what happened that day, etc.
Remember: get an attorney. A lawyer will know how to make sure you take advantage of all the defendant’s rights and protections available to you. If you cannot afford an attorney, one must be appointed for you (that’s another right you have).