Triggering a 12 v relay with an arduino
I assume you're actually trying to drive it with an Arduino output- an input won't drive anything. 

A lot of power 12V relays need around 100mA (or more) coil current. That means your base current should not be much less than about 5mA to guarantee the transistor is well saturated. If you have a 5V Arduino it might drive to 4.5V at higher current, the transistor base needs 0.7V so that's about 270uA (a lot worse if the micro is 3.3V), so it will only drive about a 5mA relay safely. From the transistor datasheet: 



Reduce the 14K resistor to something more like (4.5V - 0.7V)/0.005 = 750\$\Omega\$ and you'll be able to drive a 100mA relay safely (assuming a 5V micro).