GSM smart phones can be used in Uganda and the rest of East Africa but guests should be aware of the expensive data roaming fees that can accumulate while travelling. U.S. mobile phones using AT&T and T-Mobile will generally work in most urban areas such as Kampala and Jinja.
Remarkably, there is even cell service in many remote areas of Uganda, though it can be spotty. If you subscribe to Sprint, Verizon or another mobile service, ask your service provider specifically for a gsm phone that will work overseas.
International roaming service is not automatically enabled on mobile phones, even if subscribing to one of the services above. You will need to contact your network service provider and ask them to activate the international roaming feature. Also visit the website of your network carrier to get up-to-date information on coverage and options when travelling abroad.