首先需要在ASP.NET Core项目中安装AWS SDK for .NET包。然后，在代码中创建S3Client对象并使用GeneratePresignedUrl方法生成上传链接。最后，向该链接发出请求并获取响应即可。

示例代码如下：

using Amazon;
using Amazon.S3;
using Amazon.S3.Model;
using System;

public static async Task GetSignedURLAsync()
{
    var region = RegionEndpoint.USEast1;
    var bucketName = "your-bucket-name";
    var key = "your-object-key";
    var expiration = DateTime.UtcNow.AddMinutes(5);

    var s3Client = new AmazonS3Client(region);

    var request = new GetPreSignedUrlRequest
    {
      BucketName = bucketName,
      Key = key,
      Verb = HttpVerb.PUT,
      Expires = expiration
    };

    string url = s3Client.GetPreSignedURL(request);

    var httpClient = new HttpClient();
    var response = await httpClient.PutAsync(url, null);

    if (response.IsSuccessStatusCode)
    {
        return url;
    }
    else
    {
        throw new Exception(response.ReasonPhrase);
    }
}