Yes they can, however the terms of their visit would be at the discretion of your host Rotary District and are usually outlined in a letter that your host district sends you before you leave on your exchange. For example, often districts prefer that parents do not visit in the first 6 months. This policy helps the student to settle in with his or her host families, adjust to the new culture, and learn more of the language prior to parents' visiting.  Each host district has its own policy regarding parent visits.