No, the game will not run on 32bit versions of Windows 7. You can check below the official system requirements for both minimum and recommended versions:
Minimum System Requirements
OS: Windows 7 64-Bit / Windows 8 64-Bit
CPU: Intel Core 2 Duo E8200 2.66 GHZ / AMD Phenom X3 8750 2.4 GHZ or better
RAM: 6 GB RAM
HDD: 40 GB HD space
Video: NVIDIA GeForce GTS 450 / ATI Radeon HD 5870 or better
Sound: DirectX Compatible Sound Card
DirectX: 11
Internet: Broadband Internet connection and Steam and Online Multiplayer
Recommended System Requirements
OS: Windows 7 64-Bit / Windows 8 64-Bit
CPU: Intel Core i5 – 680 @ 3.6GHz
RAM: 8 GB RAM
HDD : 40 GB HD space
Video: NVIDIA GeForce GTX 760 @ 4GB
Sound: DirectX compatible sound card
DirectX: DirectX 11
Internet: Broadband connection and service required for Multiplayer Connectivity. Internet connection required for activation.
