Jon Custer is right if a magnet producing the magnetic field is present.
But imagine a more interesting case: an electromagnetic wave hitting a charged particle in empty space. The particle experiences a force due to the em fields. Which body experiences the reactio? Clearly, none, since there are no other bodies present. Does this violate newtons third law? Clearly, YES.
Newton's Theory is concerned with the interaction between physical bodies, not with fields. Newton did not know about such thing as a electromagnetic wave or a electromagnetic fields. His theory can not cope with such thing. Eventhough @my2ct pointed out that this is trivial for a physicist it's worth noting for anyone starting to do physics. Any theory has it's limitations.
On a side note: You could ask, is at least momentum conserved? The answer is yes. One might ask "how can this be, there are no other bodies around, clearly conservation of momentum must be broken when the charge just starts moving. You're claims are nonsense!"
In the newtonian world this critcism is valid. But in a more refined theory, the one of classical electromagnetism, we assign momentum to the electromagnetic field itself.