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As long as the total supply across the V- and V+ pins is within range it will work normally as an amplifier.
What you have to be careful of is the input and output voltage ranges. You must never feed it an input voltage outside the range of its supply so for example you run it with 0V ground on the V- supply and say +12V on V+, you can't feed it any negative voltages and you can't expect any negative voltage out. If you wish to use it as an amplifier, the trick is to AC couple the input signal (through a capacitor) and bias the input at half supply voltage with a potential divider. This will make the output pin sit at half supply and be able to go up and down in voltage so it can carry AC signals.
You could have done a forum search before posting. This is how a forum is meant to work: discussion in public, so that many people read the posts and get answers.
The question is far from being clear. What does "use single power supply" exactly mean? How is the single supply voltage referenced to circuit ground?
If you simply omit the negative supply and keep anything else, the circuit will most likely not work. You should check if OP input and expected output voltage are in specified range over full signal swing.
If you bias inputs near Vcc/2, don't use large R values unless you balance Rin Thevenin equiv values to minimize Iin*Req input offsets and/or use offset adjust, then any basic design can be operated that does not exceed specs.
Happy 50th Anniversary to the LM324 predated by the 741 and 101
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