Would A 1080p 120hz Monitor Be Worth It?

Is my pc even capable of utilizing a 1080p 120hz monitor? Or would I never be able to hit 120fps at 1080p?

CPU: AMD FX-8320 3.5GHz 8-Core Processor
Motherboard: ASRock 970 Pro3 R2.0 ATX AM3+ Motherboard
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1866 Memory
Storage: Hitachi Ultrastar 1TB 3.5" 7200RPM Internal Hard Drive
Video Card: XFX Radeon R7 260X 2GB Core Edition Video Card
Case: NZXT Source 220 ATX Mid Tower Case
Power Supply: Corsair CX 500W 80+ Bronze Certified Semi-Modular ATX Power Supply
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit)
Wireless Network Adapter: Asus PCE-N10 802.11b/g/n PCI-Express x1 Wi-Fi Adapter