Assuming you went from regular old filament bulbs to LEDs, the turn signal is flashing rapidly because there's almost no current going through the LEDs compared to a regular filament or halogen bulb. When the original bulb burns out, it passes no current at all. The computer senses the lack of current relative to its programmed reference current and activates the rapid flash.

You need to put a resistor in the line to make the lights stop flashing quickly that equals the resistance in the old bulb. The resistance can be found with a multimeter. A relay won't do this unless it also has a resistor in the circuit that replicates the resistance.  

I wouldn't change the bulbs to LEDs. They don't save meaningful amounts of energy in your car (converting to LEDs isn't boosting your gas mileage to any degree). Bulbs don't burn out every other week, etc. but that's just me. Adding resistors negates an energy savings anyways.

I recommend putting the original bulbs back in, no advantage to LED turn signals. 

If you really like the look of the LED, get ones with a built in resistor. But after doing a price comparison, the standard bulb is probably a better move.