Yes, but you won't like it.
You need to have a screen resolution higher than 1024x768. Then add the following lines into the .ini file for the game you're playing:
Video Mode=1024
KeepRes=1
This will force Civ3 into a 1024x768 non-moveable window in the upper left corner of your screen. You still have access to the task bar and start menu, but you can't move the screen.