Hi Colleen, You can't use the web API directly, but there are some workarounds (.net/java interoperability). You can create a java web service, expose the methods you need in the API as web methods and call them from your .net code. You might also consider a secure web service in case you need some extra security.
There are also 3rd party tools that use "Bridging Technology" (JNBridge, J-Integra). These are commercial products.
Another alternative would be IKVM, which is an implementation of java for the .NET framework that includes a tool that compiles java classes (and .jar files) into a .NET assembly. I tried this option but I had a lot of problems coverting data types, so I'll go with the web service.