NXP LPC GPIO Glitches on every power up. How to solve?
Start up state of a gpio is usually defined as input, potentially with a weak pull. In general, you should always design circuits so that they will not malfunction if the controlling pin is hi-z. This might be an external pull down resistor, or it might be controlling the enable input of whatever the pin connects to. It looks like your pin is rising with the circuit voltage. It is good practise to hold all ics in reset until the power is stable. There are chips designed specifically for this - see mcp130 for example. 

If you post a schematic we can be more helpful