A simple way to achieve this effect would be to launch the missile with an initial velocity of (ship's backwards vector + ship's rightwards vector), then apply a constant acceleration of (ship's forward vector) each frame, until it reaches some maximum forward velocity.
Of course, that describes a "dumb" rocket that always follows that (rightward) trajectory. If you're looking for a "homing" rocket, you can achieve that by launching with only (ship's backward vector) as the initial velocity, and applying the acceleration in the direction of the target (instead of just forwards) every frame instead.
If the engine you're using doesn't give you your ship object's directional vectors for free (Unity's transform.forward is a godsend for this sort of task), then you'll have to calculate them yourself. Given the ship's rotation as a number of degrees from some starting angle, and the ship's forward and rightward vectors when at the starting angle, you can calculate the ship's forward and rightward vectors at the specified rotation like this:
rotated_vector_x = original_vector_x * cos(angle) - original_vector_y * sin(angle);
rotated_vector_y = original_vector_x * sin(angle) + original_vector_y * cos(angle);
For further reading, I highly recommend the Wolfire Games blog posts on "Linear algebra for game developers", which begin here. Part 3 contains a description of calculating and applying basis vectors, which is pretty much exactly the problem you're trying to solve here.