draw•er "dro(-e)r\ noun (14c)
1 : one that draws: as
a : a person who draws liquor
b : draftsman
c : one that draws a bill of exchange or order for payment or makes a promissory note
So, “drawer” is perfectly correct, even if it sounds rather awkward.
Interestingly enough, Webster’s Revised Unabridged Dictionary (accessed through dictionary.com, the second definiton reached when the word is searched for) lists the usage in question as the second definition of the word. It seems uncommon, though, and might draw glances or ‘corrections’ from the wrong crowd.
Damnit, as Geobabe has cited, the relevant defintion is the second section of the first defintion, not the second definition. Geobabe slightly shortened the listed definition, though. The full definition can be found a little way down this page: ‘drawer’ at Dictionary.com
I simply c&p’d the definition from my dictionary program. The only bits I snipped out were the definitions as related to containers and underpants, as I felt they were not germane to the OP (though were this MPSIMS, those would of course be relevant ;)).
You can say “sketcher” or “penciller”, if you want (if they use pencils).
If you want to distinguish between “drawing/painting” and “acting/writing/etc.”, you can say “visual artist”. However, speaking as one who draws often (and is often called a “drawer”), it is preferential to simply being dubbed an “artist” than having much slurring and spittle-spraying being induced at your expense.
Ahh, the benefits of being multitalented. When I was in theatre, those who had on-stage skills but no off-stage skills were “actors.” Those who had off-stage skills but no on-stage skills were “techies.” Those blessed with both got the handle “theatre people.”
I was a techie with enough writing talent to get me on stage when I wrote the play, so I kind of cheated my way into the “theatre people” category.
Visual artists have it much harder. First off, most of them tend to go by “artist” with non-artists because that most non-artists think of visual arts when they think “artist.” Secondly, within a group of artists, there are those who primarily draw who feel, like PurpleHeadedYogurtSlinger, that ‘artist’ is too vague a term to describe what they do. The various suggestions are all good if they are accurate for the person’s talent. When you get right down to it, though, there’s no solution quite as good as just saying it differently.
Instead of “I not a very good drawer” try “I don’t draw well.”
I guess I’m not understanding what’s so wrong with saying “drawer,” but I think the best suggestion so far was from KneadToKnow–try “I don’t draw well” or “I’m not good at drawing.”