The proper translation for English "to spell" is deletrear. This verb comes from letra, and means both "to write a word letter by letter" and "to read a word aloud letter by letter". But deletrear is normally not thought of as a skill; it mostly appears in commands (i.e. when asking people with difficult-sounding names to spell them). If you are not a good speller (that is, your orthography is faulty and you make mistakes when writing words), you can say:
No sé escribir bien. = "I don't know how to write well."
Note that for skills you use saber, no poder (so it's not as in English). No puedo escribir suggests that you are physically unable to write or that you're barred from writing (e.g. you don't have time to sit down and write, or you are forbidden to write).
There's no way to mark the difference between the meanings of escribir as "to spell, to apply orthographic rules" and "to write, to compose a text". This must be resolved by context. If you are asked to write a speech or a piece of news and you don't trust yourself for this task, you can say:
No soy buen escritor.
but if you say
No sé escribir bien.
that will also work, since the meaning should be obvious (unless you're in a place with a high rate of illiteracy, which is fortunately less and less likely these days).
Bear in mind that, contrary to what happens in English, correct spelling is not a burdensome task in Spanish. Sure, there are ample opportunities for orthographic mistakes, but our orthography is fairly straightforward, so maybe that's why we don't place that much emphasis on a specific verb for spelling outside the limited usage range of deletrear. (That's also why there are no spelling contests in Spanish-speaking countries.)