A mid ranged PC can run Gal Civ 3. To get reasonable frame rates you will likely want an Nvidia GTX 460 or better graphics card. A more powerful CPU will help resolve the CPU turns more quickly in the later stages of Galactic Civ III. Add at least 6GB of system memory to get the best performance.
Gal Civ 3 is a 4X strategy putting the player in the 23rd century. You must research tech and conquer planets while fending off alien species doing the same.