There is no way you can get the chainsaw as a regular weapon. The chainsaw does not take up the slot of your main or backup weapon and does not play like the knife or grenade which can be used when needed but instead acts similar to a power-up. There is no special icon for the chainsaw power-up, you just have to find it in an ammunition crate on select levels and use it to help you get through difficult sections in them. Remember to use the chainsaw sparingly as it only has a certain amount of gas, the most effective time to use it is when there is a group of zombies clustered together.
You can find the location the ammunition crates by searching the horizon for green plumes of smoke. Be weary when you approach one though as they tend to be surrounded by zombies. The following video will show you where you can find an ammunition crate that contains a chainsaw.