Yes, it can and has been done. However, be aware of what you are purchasing because not all LED's are the same. Plus they require a specific way to power and wire them together.
LED's are Light Emitting Diodes. They run on a DC current. If wired up incorrectly they will either not work, work poorly or they could self destruct. You would have to be sure that the LED's put out the correct light amount and proper spectrum, that you have a sufficient quantity to complete the project and that you have a power source capable of handling the load. There is also the issue of having to calculate and add resistors to the circuits to control current and to drop the voltage to the correct level if necessary. What I mean is, many LED's run on anywhere from 3 to 5 volts DC. If your power source puts out 12 volts, you would have to find out what resistors you would need to drop the voltage down enough to protect your diodes. A 5 volt power source could give you the correct voltage, but may not handle the current requirements. The requirements all depend on what you decide to use for your lights. Start with the LED's specifications and build from there. Note that most of the LED's people use for aquariums are kind of expensive.
As you can see it can get a little complicated, but it CAN be done. You may be able to do some research and find some projects that others have done to give you a head start.
Good luck!