Yes, you can.
You can most certainly get pregnant on the last day of your period. Though it would be uncommon to ovulate at this time (remember sperm can live for 5-7 days in the vagina), every woman's cycle is different. A single woman can even vary from cycle to cycle with diet changes, stress, exercise changes, tons of things. There's no time you absolutely *won't* become pregnant in your cycle, just lower/increase the chances.