'sign me up' is a correct and usable phrase in written English. You can use it when someone is asking to be included in an activity or event. For example, "I heard there's a new running club in town, sign me up!".
So sign me up for the crusade.
If this be butchery, sign me up as an apprentice.
And so I insisted that my parents sign me up for a sailing class".
So sign me up for a memoir on my alliance with Dr. King.
They signed me up for some magazines.
They signed me up for an Indian matrimonial site.
It was my niece who signed me up for Silverline.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union