AWG for connecting a USB
USB specifies 28 AWG for the signal pair, and 28 to 20 AWG for the power pair. Note that 28AWG is rather thin for supplying 500mA (the maximum current that USB 2.0 specifies for power), and will result in a high voltage drop for long cables. Most USB cables use 26 or 24AWG for the power pair, or even bigger (typically 22AWG) for the longer ones (~3 meters).

As Passerby said, Ethernet is usually between 22 to 26 AWG.

But it is not only about the AWG. USB cables are supposed to have 90Ohm impedance, and ethernet 100. The impedance mismatch could be a problem for long cables, especially if you use it as an extension to another regular 90Ohm USB cable. USB High Speed will be more sensitive to this than Full Speed.

In short, it will most likely work, except if you're making a very long cable, but you'll definitely be violating USB specs.