No, but kind of yes.
Standard electromechanical relays physically require current to function. But that current doesn't have to come from your 3 V signal--you can use it to switch a MOSFET to connect some other power supply to the relay.
simulate this circuit – Schematic created using CircuitLab
With a configuration like this, and a suitably chosen MOSFET, you can use the current from the 3 V supply to actuate the relay, while requiring only enough current from the signal to drive a 10 kΩ resistor (which you can even omit, if you can be sure the signal will never be left floating).
You can also use a 12 V relay, since you definitely have a 12 V supply available, as long as the MOSFET is chosen accordingly.
The DMN2058 shown here will definitely work for any 3 V or 12 V relay, but depending on the relay's current requirements you may also be able to use a cheaper one like a DMN63D8 or NX138/BSS138; you can find information on choosing a MOSFET elsewhere on this site so I won't go into any more detail than that. Even the DMN2058 is still only $0.38 right now, so "cheaper" literally only means saving a handful of pennies.