Try something like this:

using System.Linq;
using System.Web.Http;
using System.Web.Mvc;
using System.Web.Routing;
using Umbraco.Core;

namespace MyNamespace
{
    public class MyApplicationEventHandler : ApplicationEventHandler
    {
        protected override void ApplicationStarted(UmbracoApplicationBase umbracoApplication, ApplicationContext applicationContext)
        {
            RouteTable.Routes.MapHttpRoute(
                "MyCustomApiRoute",
                "MyApi/{controller}/{id}", new { id = UrlParameter.Optional });     
        }
    }
}