I need to buy an access point. The available one is Aironet CAP 1602-E . My question is do I need a WLC to use this access point or can I use it alone?
The model you've quoted is a "CAP". It prefixed with a "C" which stands for Controller-based. You can get one with "S" and this stands for Stand-alone.
If you've already ordered the part then you can easily convert the AP to operate in autonomous (or stand-alone) if, AND ONLY IF, you are able to download the autonomous IOS. If you can't download the autonomous IOS, ask the vendor who sold you the AP and see if they can provide you with the IOS file.