Deploying an Arduino Uno R3 standalone
So you would rather use your Raspberry Pi than your PC? Easy, as it
turns out that a Raspberry Pi is not that different from a PC running
Debian or a Debian-like OS (e.g. Ubuntu).

Just connect the Uno to the Raspberry Pi through the USB link. Log the
data on your Raspberry exactly like you would do on the PC. You don't
need any Ethernet or WiFi shield. You just need to make sure that
whatever logging program you use on the PC can run on the Raspberry Pi.
This is most often trivial if the PC is itself running a Linux distro.