Can a Mosfet be used on a grounded solenoid

Noob question,

I have a solenoid that draws 600mA. Can I power it from an Arduino using an output through a mosfet when the solenoid ground cannot be wired through the mosfet.
All diagrams I see have unswitched positive to the solenoid and the ground is wired through the Mosfet.

What would be the best course of action?

The solenoid if 5V? 600mA is more than Arduino supply can supply without overheating.

Use a separate power supply and a Logic Level gate, Low Rds P-channel MOSFET to source current to the solenoid coil (which has the other side connected to Gnd with the power supply side Gnd).

What you are looking for is called a high side switch. It can be made with a P channel MOSFET and a bipolar NPN transistor. Here is an example of the high side switch. Replace the motor with the solenoid, Be sure to keep the flyback diode. The component values need to be changed to meet the requirements of your circuit.

This one can be driven without the NPN if you have a 5V supply to the solenoid.
https://www.digikey.com/product-detail/en/fairchild-on-semiconductor/NDP6020P/NDP6020P-ND/1055922

I would buy a pre-packaged "high side switch" such as a BTS716G. That puts a lot of circuit protection and specialist driver circuitry into one easy-to-use package.

Thanks for all the info!

Interestingly, the BTS716G High Side Mosfet switch uses an N-Channel Mosfet design.
Traditionally, on the High Side, P-Channel Mosfets are a more common sight.

If you can afford a step-up voltage converter then an N-channel is more efficient. The holes are less mobile than the electrons. That's one of the reasons for choosing an integrated chip like that.

Also,

How do I calculate the resistor sizing for say a P channel mosfet high side switching application?

220 for the Arduino to drive the gate. 10K pullup to hold the gate off during Reset.
Gate is like drive a capacitor, which looks like a short to start.
So 5V/220 ohm = 22mA to drive it high, or low. Can go a lower, like to drive 35mA. Some argue the resistor is not needed as the transition time is short enough to not damage the output. Good engineering practice says to have one.
10K for minimal current to hold a known state when nothing is driving the gate.