Can I sort the songs in a playlist on my iPhone?

Im sorry, but in my knowlege there is no way to change the sorting in the way that you describe. The only close solution that i know of would be to edit the playlist manually, by pressing the "Edit" button in the top of the playlist, press and hold the three gray stripes on the right side of a chosen song title, and move it to its intended location within the playlist.

There is a round about way to do this. First, go to the playlist you want to sort and sort it. Next crate a new playlist. Leave it titled as playlist for now. Go back to your original playlist and drag the now sorted songs to the newly created playlist. Once that's done, the songs will be in the new playlist in the order you wanted them. Go ahead and delete you original playlist, then rename the new one to the name of the original playlist.