That's a transistor, not resistor. (Like a relay - a small Base current controls a larger output current.)
Almost any NPN transistor like the 2N2222 that can supply probably at least 250mA for the relay. (500mA or 1A rated would be better.)
But there should be several relay driver circuits on the web - usually 2 resistors and a transistor. Plus maybe a spike suppression diode across the relay coil...
A nice alternative may be a FET - specifically a MOSFET. That is a voltage controlled transistor - instead of current, it is voltage that controls a FETs output (resistance).
WTF does that mean?
Instead of needing maybe 5mA into a transistor to turn on up to 500mA current (ie, a gain aka Beta (β) of 100), a MOSFET only needs nA or uA (nano- or microAmps) to turn on several Amps. A $3 MOSFET may handle 100A! (Hence no need for a relay - if the MOSFET on resistance is low enough, hence an acceptably small voltage drop.)
MOSFETs are a high-impedance input, hence no input resistor is needed, though usually a resistor is inserted to guard against certain problems. No fussy - a low Ohm resistor between (say) 47 Ohm to 1k should be fine.
But you might need a "pull down" resistor to make sure it turn off. High-impedance means any small charge is enough to turn the FET on, hence keep it grounded. (Specifically a resistor between its Gate and Source. Its Gate is the equivalent of the transistor's base; like a relay's coil (that turns on a bigger current).)
Again, not fussy, but typically a 1 MOhm (megaOhm) resistor is used.
Alas, no time for details, but maybe search "MOSFET relay drivers" or similar (tough that might return the many MOSFET driver chips (Integrated Circuits; ICs) that are available.
Wiki has good info, and probably suitable circuits as I recall, though one of their MOSFET articles is heavily "theoretical" (blah!) whilst another is nice and basic(ish). Probably the same for Wiki transistors.
BTW - a FET typically needs 5V to turn it on fully, so any 12V signal is ample.
And transistor needs more design - you have to size the input/Base resistor to supply whatever mA (times its gain) to allow enough output Amps, and the base must be below ~0.6V to be off, and above ~0.7V to be on. A FET switch is merely greater than (say) 5V to turn on - no current gain is involved - hence why the input resistor is irrelevant (it merely limits current if the Drain current somehow flows thru the Gate in certain situations - or something like that, but I'm sure Wiki covers that, but probably in a more confusigated manner even than my verbiage!).