Most smart phones now come equipped with a front facing camera feature, specifically for taking selfies. Sometimes, the software isn't pre-loaded. You might be able to download an app to to do this for you, if your phone already has a built in front camera. If you don't have a front facing camera, or if you prefer taking selfies with the other camera, there is a better way to do it.
Yes, your mirror is reflective. Your smartphone also has a huge screen that the camera uses for a viewfinder. Put two-and-two together.
Hold the phone like this ^
1. Stand back, away from the mirror.
2. Flip the phone around, and point the camera towards you.
3. Use the mirror to look into the huge view-finding screen on your phone.
4. Use your volume or home button as the shutter to capture the photo.
5. Enjoy your selfie, sans the additional bragging. Because everyone knows you really just want to show off your ridiculously expensive phone.
6. (Optional for bonus points) Practice without the mirror. Take about 5 mirror selfies, and pay attention to exactly where you need to hold the phone each time. Get an idea of where you would need to position it, if you didn't have a mirror nearby, then try a few times without.
You don't have to hold the phone out over your head to get a great angle. With enough practice, you can figure out which position works best for you, and you'll be a Selfie Pro in no time.