An unlocked cell phone will work in Uganda, but be sure to contact your service provider before you travel to add global roaming to your plan.
Alternatively, you can purchase a prepaid SIM card and use your unlocked phone while in Uganda. SIM cards are available at the airport right after immigration or at the nearest phone store, such as MTN, Airtel, or Lyca Mobile, on your way from Entebbe International Airport. Most Cafés, hotels, Lodges and some restaurants in the cities also have WiFi in case you want to get online on the go.