It is most likely possible, but ASP.NET is typically C# or VB.NET. Powershell is basically a wrapper, written in C# to interface with .NET. Server-Side code would run in C#\VB.NET, so you can run things directly in C#\VB.NET rather than use Powershell. If you are taking a Powershell script that is text or upload and executing that, that is also possible to execute scripts via C# or VB.NET.
How to execute PowerShell script or cmdlets from C# code? · GitHub
Keep in mind that running something in ASP.NET is running in IIS and security controls will normally not like a web service trying to execute things locally on a server. Then you get into permissions, user elevation, running the script as or other things it will get complicated very quickly. Most of the time you would have an agent or service running on the server separately from the website to execute that code and return a result via an API.
I’ve see solutions where they have Powershell containers on the website and can execute code via agent proxies for RPA. It is possible, but there are many security issues to plan for depending on what you are trying to accomplish.