Yes, the camps have power, mostly as solar lighting and/or a generator. The power may be switched off for part of the day. At small camps and lodges you may not be able to use a hairdryer or electric shaver, but batteries can be charged either in your tent/room or in a communal area.
Your charger must be 220v or you will need to bring a transformer, though most electronic equipment now automatically converts from 110v to 220v. The required adaptor plugs are included in most international travel adaptor kits. For Kenya it is plug type G (the British-style plug with three rectangular pins). In your safari vehicles there is often the possibility to charge your phone or camera if needed.
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