An Intel Core i5-2500 CPU is required at a minimum to run Call of Duty: Modern Warfare. However, the developers recommend a CPU greater or equal to an Intel Core i7-6700 to play the game. Provided that you have at least an AMD Radeon R9 380 graphics card you can play the game.
The hardware you'll need to meet the Call of Duty Modern Warfare 2 recommended system requirements isn't that much higher. Crafting a team of 12GB of RAM and a processor as powerful as the Intel Core i7 4770 or AMD Ryzen 5 1400 will help maintain higher minimum and maximum frame rates.