It doesn't need to be something that specifically targets asp.net core
You could use some something like
step 1:register a new site on Google
To begin with, you will need to register a new site on Google. Once that is done, you should have your Site Key and Secret Key with you.
https://www.google.com/recaptcha/admin/create
https://www.google.com/recaptcha/intro/index.html to add captcha to your .net core project.
You can use Google recaptcha instead of implementing your own. Here is one implementation - http://dotnetthoughts.net/how-to-implement-recaptcha-for-asp-net-5/
ou can try this.
http://dotnetthoughts.net/implementing-basic-captcha-in-asp-net-5-mvc-6/
I didn't tried it in ASP.NET Core RTM. I developed it in ASP.NET Beta 6 Days. Please go through the below nice link to implement Capcha in ASP.NET application:
http://www.c-sharpcorner.com/UploadFile/0c1bb2/create-captcha-using-google-recaptcha-in-Asp-Net/
You can use the following nuget package. NuGet Package: https://www.nuget.org/packages/PaulMiami.AspNetCore.Mvc.Recaptcha/
Source Code: https://github.com/PaulMiami/reCAPTCHA
I hope this helps you. Regards, Manoj Kulkarni
Blog:http://dotnetcontext.com.
Useful links:
https://www.dotnetfocus.com/how-to-add-google-recaptcha-to-your-net-core-project/
https://www.cnblogs.com/stulzq/p/10714417.html (chinese step by step)