.NET Core on Raspbian/ARM?

.NET Core 2.1 supports Raspberry Pi.

Here is how to install .NET Core 2.1 on Raspberry Pi:

$ sudo apt-get -y update
$ sudo apt-get -y install libunwind8 gettext
$ wget https://dotnetcli.blob.core.windows.net/dotnet/Sdk/2.1.300/dotnet-sdk-2.1.300-linux-arm.tar.gz
$ wget https://dotnetcli.blob.core.windows.net/dotnet/aspnetcore/Runtime/2.1.0/aspnetcore-runtime-2.1.0-linux-arm.tar.gz
$ sudo mkdir /opt/dotnet
$ sudo tar -xvf dotnet-sdk-2.1.300-linux-arm.tar.gz -C /opt/dotnet/
$ sudo tar -xvf aspnetcore-runtime-2.1.0-linux-arm.tar.gz -C /opt/dotnet/
$ sudo ln -s /opt/dotnet/dotnet /usr/local/bin
$ dotnet --info

According to discussion here sample solution is working on Raspbian. Official instructions are here.

Personally I'm using Ubuntu Server Standard as in this guide but I suppose that is not linux for raspberry as mentioned in your question.