If your digital music is all standard rez mp3s from iTunes then it is possible that a external DAC might not make much of an improvement.

The DAC would need to be connected to your integrated amp inputs.

The phone only has analog output through the headphone jack, no DAC needed to feed your stereo.

Jackfish might be right.  If you're only streaming from iTunes cloud it's possible the bit depth and sample frequency aren't even CD quality (16-bit 44.1 kHz) and so a DAC might not help.  Or at least not much. 

But Apple has startedoffering higher quality files. And depending on your music preferences there are plenty of sites, like HDTracks, that offer hi resolution downloads. You might want to try those since you take listening seriously enough to stick with vinyl.

There are several inexpensive USB DACs and some will allow a 30-day trial if you want to test it out. 

Scott