Migrate from .Net Framework Ado.Net to Net Core

I was worndering... Should I upgrade a project .Net Framework that's primary based on ADO.Net with lots of procedures to .Net Core? Is there even a way to do it?
Is there a way to do it without having to go into entity framework mode when developing.
I want it to stay with the way we call proc and that's it.
Thanks.

You can and should do this. There are a lot of nice new features included as part of Core, including some significant performance wins, and while it hasn't been formally announced yet the intent is clear Core is the future and Framework is the past; there will likely come a day when Framework is no longer supported and you will need to do this at some point anyway. The sooner you make the transition, the less "drift" you'll have to worry about between the two platforms and the easier the migration will be.

For ADO.Net, specifically, the main trick is the providers have moved. While they are still available, the namespace is different (ie: Microsoft.Data.SqlClient instead of System.Data.SqlClient) and they are not included out of the box but must instead by added from NuGet. Aside from this fairly simple change other ADO.Net code should continue to work as before.

Beware, though, you might also find a few other non-ADO.Net things have also moved or changed in the transition from Framework to Core (WinForms, Security/Cryptogaphry APIs, and identity come to mind just at the beginning), so this can still be a significant undertaking.