To retrieve data from a third-party API in an ASP.NET Core Web API application, you can use the HttpClient class, which provides methods to send HTTP requests and receive responses. Here's an example of how you can do it:

1. Add the System.Net.Http package to your project. You can do this by right-clicking on your project in Visual Studio and selecting "Manage NuGet Packages." Then search for and install the System.Net.Http package.

2. In your ASP.NET Core Web API controller, create an instance of the HttpClient class to make the API request. Here's an example of a GET request:
   

using System.Net.Http;
using Microsoft.AspNetCore.Mvc;

namespace YourNamespace.Controllers
{
    [Route("api/[controller]")]
    [ApiController]
    public class DataController : ControllerBase
    {
        private readonly HttpClient _httpClient;

        public DataController()
        {
            _httpClient = new HttpClient();
        }

        [HttpGet]
        public async Task<IActionResult> GetData()
        {
            // Replace "API_URL" with the actual URL of the third-party API you want to access
            var apiUrl = "API_URL";

            HttpResponseMessage response = await _httpClient.GetAsync(apiUrl);

            if (response.IsSuccessStatusCode)
            {
                string data = await response.Content.ReadAsStringAsync();
                // Process the data or return it as-is
                return Ok(data);
            }
            else
            {
                // Handle the error condition
                return StatusCode((int)response.StatusCode);
            }
        }
    }
}

1. Replace "API_URL" with the actual URL of the third-party API you want to access.

2. In this example, the GetData method sends a GET request to the specified API URL. If the request is successful (HTTP status code 200), it reads the response content as a string and returns it as the API's response. Otherwise, it returns an appropriate error status code.

Note that you may need to configure additional settings for the HttpClient, such as base address, headers, or authentication, depending on the requirements of the third-party API you're accessing.