You will need to modify a line in the Alpha Centauri.ini that is located in the game folder. To do this:
Double click on My Computer
Double click on the C: Local Drive (your Hard Drive or the drive that the game is installed to)
Double click on the Program Files Folder
Double click on the Firaxis Games Folder
Double click on the Sid Meier's Alpha Centauri Folder]
Double click on the Alpha Centauri.ini File (The file looks like a read me text file with a little gold symbol on it).
Once the file is open in Notepad, change:
Be sure to save your changes, then run the game. You may still receive the error message. If it occurs, click OK and the game will load fine.
If you are Installed Sid Meier's Planetary pack then their will be no Alpha Centauri.ini File initially. Upon attemping to play the game and clicking ok despite CPU being unsupported the ini file will be produced. Then simply change the ForceOldVoxelAlgorithm to 1.