You don't 'inject' IoC into anything. Inversion of Control, or more specifically Dependency Injectionmore specifically Dependency Injection, is a technique where you inject services into consumers - preferably via Constructor Injection.
In ASP.NET, all you need in order to do that is a custom IControllerFactory. You can, however, implement that IControllerFactory with a DI Container to make things a little easier. Here's a list of various DI Containers for .NETa list of various DI Containers for .NET.