Regulated input relay switch
Two issues with your circuit:


If you want a well-controlled and accurate turn-on threshold for your relay, you should probably use a comparator at the input to be sure the switching happens at the voltage you want it to happen at. There are other possibilities, but a comparator is the most straightforward and foolproof one.
If you want to switch on a 12 V relay, you need to apply pretty near 12 V to the coil. 10 V or 11 V might work (the minimum "must operate" voltage will be specified in the relay datasheet if you are buying from a reputable manufacturer). But your circuit is only applying 4.3 V or so, and that's not going to work well at all.

If you want to use an NPN BJT to buffer the output of a comparator to drive a relay, you'll most likely want to connect that BJT as a low-side switch between the relay coil and ground, for example as shown in this prior question.