It doesn't need to be something that specifically targets asp.net core 1.0
You could use some something like
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.
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:
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