It's been done, even back in 1995:
View attachment 3906
This puppy is called the 'Mikrosol' and according to an article I read some years ago it was the first RC plane to be directly powered by solar cells (rather than utilise the solar cells to charge an onboard battery).
You can read more about it and the subsequent models here (if you know German or google translate):
http://rz-home.de/~sieghard.dienlin/
Or you could buy a glider. Sun warms earth, earth warms air, warm air rises and causes thermal, RC glider rides thermal. Voilà - solar powered flight!