NOTE: I would only recommend this solution in a very limited number of scenarios. Single server / simple development and test scenarios are the most likely. If you have a production farm with multiple servers I would recommend taking a look at alternatives that are better supported (self hosted apps for example).
With that in mind, if you don't need any integration with SharePoint but just want to host your Web API in the same site you can create an application off the root of the SharePoint site. Then just add the correct sub directory to your path.
If you where using http://sample.com/api/value, use http://sharepoint.com/subapp/api/value.
