This is up for debate in modern English, older styles state that their is explicitly plural, so "his or her" should be used instead. However many people find it easier to just use they/their/them rather than "he or she"/"his or her"/"him or her".
There is not a definitive source on what is right or wrong in this case - as language is spoken by the people and forever changing. But know that almost everyone will know what you mean if you use they/their/them as singular. Also use "he or she" et. al. does not really sound natural to me unless it is technical writing, or a public announcement, or something slightly formal where a person would be reading off of text.