DotA 2 Minimum System Requirements:
OS: Windows® 7 / Vista / Vista64 / XP
Processor: Pentium 4 3.0GHz
Memory: 1 GB for XP / 2GB for Vista
Graphics: DirectX 9 compatible video card with 128 MB, Shader model 2.0. ATI X800, NVidia 6600 or better
Hard Drive: At least 2.5 GB of free space
Sound: DirectX 9.0c compatible sound card
DotA 2 Recommended System Requirements:
OS: Windows® 7 / Vista / Vista64 / XP
Processor: Intel core 2 duo 2.4GHz
Memory: 1 GB for XP / 2GB for Vista
Graphics: DirectX 9 compatible video card with Shader model 3.0. NVidia 7600, ATI X1600 or better
Hard Drive: At least 2.5 GB of free space
Sound: DirectX 9.0c compatible sound card
According to one of the members of DotA 2 staff, in case you can run Alien Swarm, you will be able to run DotA 2 since both games require same System specs to be played.