The system requirements for the StarCraft II Beta are as follows:

Minimum Requirements:
Operating System
Windows XP / XP64 (Service Pack 3)
Windows Vista / Vista64 (service Pack 1)
Windows 7 Home Premium
Processor
Intel Pentium IV 1.3GHz
AMD XP 1500+
Memory
(Windows XP) 512mb
(Windows Vista) 1024mb
(Windows 7) 1024mb
Graphics
3D graphics processor with Hardware Transform and Lighting with 32 MB VRAM
such as an ATI Radeon 7200 or NVIDIA GeForce 2 class card or better
Hard Drive
15Gb (of free space) -
DirectX
DirectX9.0c

Recommended Requirements:
Processor
Intel Pentium D
AMD 64 X2
Memory
(Windows XP) 1024mb
(Windows Vista) 2048mb
(Windows 7) 2048mb
Graphics
3D graphics processor with Vertex and Pixel Shader capability with 128 MB VRAM
such as an ATI Radeon X1600 or NVIDIA GeForce 7600 GT class card or better