Most likely. It's an older game that doesn't require much in terms of hardware. Post your specs for a better answer.
System Requirements (Unreal Tournament 3 Black on Steam)
Minimum:
Supported OS: Windows XP SP2 or Windows Vista
Processor: 2.0+ GHZ Single Core Processor
Memory: 512 MB RAM
Graphics: NVIDIA 6200+ or ATI Radeon 9600+ Video Card
Sound: Windows Supported Sound Card
DirectX: DirectX 9.0c
Hard Disk Space: 8 GB