How can I accurately and precisely measure current in a 110V AC circuit, with a 1kohm-50kohm load, using an oscilloscope?
Edited because of new information in a later comment)

As your after a 4 wire measurement, lets begin by lowering the voltage to be within the safe range of your scope

For a 4 wire measurment you can either know the current your sourcing, and measure a voltage, or know the voltage and measure a current, due to the application, measuring the voltage will be much easier

Lets start with say a 6.3V transformer, its peak voltage will be within your scopes ability, (about 9V peak), we only need to know the amount of current so we will use a current shunt resistor to measure it, as the current will be low due to the resistance of the soil we will keep it rather high, lets say about 10K,

1 scope probe attaches across this current shunt and gets the current via measuring a voltage, now the scope probe will shift this value slightly due to acting like a 1M or 10M resistor in parrellel, but the effect can be calculated out.

So 1 probe to 1 side of the transformer, 1 probe via the current shunt to the other side, and we have out "Source" probes

Next up the measure, due to the small amount of current, we will use amplification to make up for it. using a "differential amplifier", these have a fun side bonus that its easy to choose what voltage is outputs that difference against, you will need to provide power to this device, so may need to build a small rectifier and capacitor to feed it DC voltage off the same transformer

The relationship for the gap between the probes is important so you may wish to mount these 2 measure probes on something to keep them a fixed distance apart. 

the second scope channel measures the differential output, and you have a voltage, and a current, leaving you with a resistance, 

The input voltage minus the measurement voltage is then the soil voltage, you know the current based on the measurement voltage leaving a simple calculation for its resistance

Falstad Circuit Simulator

Now this is a not so normally used differential amplifier design, but it is one of my favorites for high impedance work, as for a specific op amp, you want one that can handle atleast +-10V (overkill but much harder to damage) sadly its getting late, so none are coming to mind.