We know .NET Core supports Linux x64 and x86, MacOS X, Windows... but is it ready to use in Linux for Raspberry Pi? (Raspbian, for example).
.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