If your computer is Windows, this will not be possible. Just by downloading the installer yourself you will achieve this.
If it’s Linux or OS X, you can copy the folder where Studio is installed. Why in this case android does not "install" really, it just moves the files to the program directory and creates a shortcut.
Under Linux, Android Studio is usually installed by default within the /opt folder. Already in Osx go to Finder, find the shortcut of Androidstudio, click with two fingers on and select "Show Package Contents" copy the folder Contents.
But nothing will help if the other machine does not have the java installed or is of different operating systems.
Good luck!