A very crude timer can be made using a single transistor.
The delay will depend on how long it takes for the capacitor's voltage to drop below the level required to provide enough base current to switch the relay on.
The delay will depend on the capacitance, base resistor, power supply voltage, transistor gain and the relay.
EDIT:
A better timer circuit can be made using two transistors, an arrangement known as the monostable multivibrator (see Wikipedia).
An even better monostable can be made using the 555 timer IC.