To obtain the jet pack, simply enter the code 1-800-333-0100. Enter this code using the cell phone that Roman gives to Niko in the game.
To access Niko's cell phone, press the UP button to lift the phone and reveal the keypad for entering numbers. Use the arrows to select the numbers. Instead of pressing the dial button, hit the UP button once more. The message "Cheat Activated" appears on the screen to indicate that the code was successful. When the code is successful, a "Cheats" menu appears under the phone options, so one must enter the code only once.