Best use a relay to isolate the arduino from the 12V circuit. You can use one of these arduino relay-modules that you can find everywhere on the internet (Google "Arduino relay module". A single relay is sufficient).
For the 12V you need to look for a 12V power supply (SELV or NEC CLASS 2 for safety reasons). For this have to look how much current/power your door strike needs. 1A or 10W should be sufficient, maybe also less.
Then you connect the normally open working contact of the relay with the 12V on the one side and with the door strike on the other side. The minus of the door strike goes to the minus (ground) of the 12V power supply.
This should do it.