If you are looking for a solution to asynchronously load data from REST API within your windows phone app, then the below solution might be helpful for you.

public async Task<string> ReadUrlAsync(String parameter)  
  {  
       string JsonData;  
       try  
       {  
         string request_url = "https://requesturl.com/api&parameter=" + parameter;  
         var request = HttpWebRequest.Create(request_url) as HttpWebRequest;  
         request.Accept = "application/json;odata=verbose";  
         var factory = new TaskFactory();  
         var task = factory.FromAsync<WebResponse>(request.BeginGetResponse, request.EndGetResponse, null);  
         var response = await task;  
         Stream responseStream = response.GetResponseStream();  
         using (var reader = new System.IO.StreamReader(responseStream))  
         {  
           JsonData = reader.ReadToEnd();  
         }  
         responseStream.Close();  
         return JsonData;  
       }  
       catch (Exception ex)  
       {  
         MessageBox.Show(ex.Message.ToString());  
         return String.Empty;  
       }  
 }