No, the resistors are built-in.
Note that the ULN2003 is a pretty crappy part - they give the headline spec of 500mA, but in practice, the outputs only go down to like 1.4v or so even with low current, and the total current that you can have passing through the ULN2003 at any given time (based on its' thermal limits) is much lower than a naive reading of the datasheet suggests. I got a real shock (figuratively speaking) when I tried to use these for some (what I considered) light duty switching - they ain't nearly as good as you'd think based on a quick read of the datasheet by someone who isn't used to spotting how manufacturers spin their specs.
The TBD62003 is a pin-compatible, drop-in replacement that uses superior MOSFET switching elements instead of darlingtons; unless your load and/or duty cycle is really light, I suggest considering using the TBD62003 instead (there's also an 8-channel version to replace the '2803, and a P-channel version to replace... whatever the PNP version of the '2003 is called).