There is no convenient way for the Web API to send the anti-forgery tokens to the client.
Therefore, please consider using a token-based authentication and ssl as a countermeasure against CSRF attacks for the Web API.
Typically, CSRF attacks are possible against web sites that use cookies for authentication, because browsers send all relevant cookies to the destination web site.
Unlike ASP.NET Identity (cookie-based authentication), the browser will not automatically include the access token in subsequent requests. The application must do so explicitly. That's a good thing for the token-based authentication, because it limits CSRF vulnerabilities.