Too bad about RadioShack.
That was the place to go for something like this.
They are online, however.
You will need a combination of multiple adaptors, most likely (it is possible with fewer, but there is a lot going on here), and a headphone volume control (male on one end, female on the other), and a cord with a male plug on both ends.
First, you should make the size change, from ¼ in to 3.5mm A simple stereo headphone adaptor will do this fine.
Now the rest of the items are all going to be 3.5mm.
Plug the headphone volume control into the headphone adaptor, turn it all the way down, and then bring the volume on the control to 25%-33%. If there is volume control on the turntable, set it at 7 (70%).
Now, you need to combine the stereo (2) channels together into one, because as
@mikedt mentioned, the mic input is monaural.
So for this, use an adaptor that has a stereo plug on one end (male) and a mono output on the other (female).
Plug the male to male cord into this.
Finally, you need a way to move the signal from the wire that it is on (one of the two channels inside that cord, probably the left) onto the correct path for the microphone input.
This can be tricky.
There may be an adaptor, I am not sure.
What I do know, is that you could buy the actual plug, a 3.5mm TRRS (tip, ring, ring, sleeve), cut the end off of the cord, and install the new plug onto it.
When you see the wires inside the cable, there are three connections, a positive for each stereo side and a common ground.
Since you are using monaural sound, only one of the channels and the common are going to be used.
Compare the two plugs, the original and the new.
The extra connection on the new plug is the microphone positive.
Now play some sound through the setup and use a multimeter to find which wire the music is on.
That one goes to the mic part of the jack.
Connect the shield to the common connection, and disreguard the other wires.
Complete the install of the new jack.
This is the end that plugs into your phone.
Try it out, listen closely for distortion.
If you here any, then bring the volume of the turtable (if available) down to 60% and listen again.
If the only volume control is the headphone volume control, use that to turn down the level until no distortion is heard.
This volume control will be extremely touchy!
Wasn't that easy?
Now you know why
@mikedt uses a computer for such things.
I just wanted to point out that it can be done via physical means.
Heck, if you have a mixing board, the level adjustments would be even better.
I guess I also have too much time on my hands.
But in reality, you want to do your recordings more justice than what I described.
The mess above is what we did back when adaptors and parts were cheap, and mixing boards were expensive.
I dare to say that now, you could probably buy a mixing board with what you would have to invest in adaptors.
Of course, you would still need adaptors to connect your phone to the mixing board...
nevermind.
lol