Yes, of course. This is one of the main points of Banach-Tarski. Explicit constructions can be found here, for example: mathoverflow.net/questions/49363/…
– Theo BuehlerJun 30 '11 at 22:47

Dear Theo, did i missed something or the examples in these explicit constructions the generators are invertible, but not unitary matrices? many thanks
– PauloJun 30 '11 at 23:25

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@Paulo: the constructions there include an injective homomorphism into $\text{SO}(3)$, which is compact Lie, so embeds in a unitary group (in this case we can take $\text{U}(3)$).
– Qiaochu YuanJun 30 '11 at 23:27

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Using the fact that the universal cover of $SO(3)$ is $SU(2)$, together with the fact that every homomorphism of the free group can be lifted (a consequence of freeness), you can construct explicit homomorphisms of $F_2$ into $SU(2)$.
– Alain ValetteJul 1 '11 at 12:59

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Of course one could invoke the Tits alternative, stating that in characteristic 0 any not virtually solvable subgroup of $GL_n$ contains $F_2$... but that would be a bit pedantic!
– Alain ValetteJul 2 '11 at 19:46