How can I monitor my tank circuit?

What you need is an antenna, connected across the oscope leads. I would start with a simple wire. why not start with a wire and experiment? You don't say what the output power is. If the voltage output is too low, reorient the receiving antenna or increase its size. You can look up references to get the characteristic length you need for an effective antenna, a submultiple of this length should give you enough voltage to read it with a scope.