ASP.NET Core Web API allows clients to upload files as part of the HTTP request. To implement file uploads, you can use the IFormFile interface provided by the framework. In the API endpoint, you can accept a parameter of type IFormFile or a collection of IFormFile to retrieve the uploaded file(s). The files can then be processed or stored as per the application's requirements. You can configure the maximum file size, allowed file types, and other validation rules to ensure secure and controlled file uploads.