If the condition of the fringe bothers you, make it straight again with the following technique:
Using a damp, clean (not gunked up with toothpaste) soft bristle toothbrush, gently comb the fringe as you would comb hair until it lays flat and untangled. Re-dampen the toothbrush from time to time. It is best to use a flat surface for this task, such as an ironing board. It is a little OCD, but the technique works.
As for dry cleaning your scarf, it depends on the care label. Some cleaners will deliver the scarf to you with the fringe ironed flat, others will give it back the way you gave it to them. Personally I prefer to hand wash my scarves and shawls. If you hand wash, you can use the toothbrush technique to straighten the fringe while the scarf is still damp.
Hope this helps.