+1 to that, GTA IV also requires more than 1GB of video RAM if you want to max it out at 1080p. If your video RAM usage in the options screen is above 1GB, you'll have to turn some settings down in order to get acceptable framerates.
As said above, which card you have is important. Something in the upper mid range to high end like a Radeon HD 6870 or GTX 560 will do relatively well on high settings for GTA IV. Something low end like a GT 520 or Radeon HD 6450 will only just barely run the game at minimum settings. Since every card from the bottom of the barrel on up has at least 1GB of RAM these days, just saying your card has 1GB isn't helpful.