If you and her are both up to it, you sure can! There's no physical reason whatsoever that makes sex during menstruation unhealthy or unsafe. If you would prefer not to deal with much mess, she might choose to use an internal protection product like a tampon or menstrual cup, though it is not safe to have intercourse with them in; other forms of sex are fine. Otherwise, you've but to lay a towel down to protect your sheets and have at it per usual!
Her options for relatively mess-free intercourse include getting fitted for a diaphragm if she desires contraception. It's a cup-shaped device that fits in the vagina over the cervix to block sperm from entering, and has the bonus of collecting menstrual blood. Also available are Instead softcups, a brand of disposable menstrual cup that is shaped very much like a diaphragm. They only come in one size, however, and some women find they simply don't stay put or leak.
The nitty-gritty is that if you want to be sexual during her period, you both have to be okay with some degree of contact with the fluids, no matter what measures are incorporated. If you are, proceed with confidence!