ULN 2803A Relay Driver Circuit
As in the comments you need to ground GND and connect COM to Vin (power for the relays).

If you insist on using the ULN2003, there is no way around the voltage drop, so you can increase the input voltage by a volt or two, or use lower voltage relays (which will draw proportionally more current).

Alternatively, use some other kind of driver such as discrete MOSFETs and diodes (you can use duals for example) or some entirely different kind of driver chip such as TI’s TPICxxx DMOS power shift registers.