Need a single-word term for "an artist who produces drawings"
Solution 1:
I believe, the only generic apt term would be drawing artist which isn't a single word. (You can hyphenate as drawing-artist if you really want to use a single word). Many drawing art and job websites use this term. There are more specific terms like pencil artist, portrait drawing artist etc. also.
As already mentioned, the only generic single word is drawer but it is not that useful to use this term for one who draws. Additionally, it depends on what you draw and on your occupation/art etc. so there isn't a generic and useful single word. There are even cartoonists who are technically a drawing artist.
The reason why the term drawer is not common like painter and sculptor might be that painting and sculpting were prominent and established art forms in the history and there were popular and influential artists of this art form; thus there are generic and common single word terms as painter and sculptor for the artists. Drawing was more like a technical occupation throughout the history as in draftsmanship where there are specialties like architectural drafters, mechanical drafters etc. In art, it was rather an artistic practice than an established art form so we could say that a painter is/was a drawer already. Traditional drawings were simple compared to some modern drawing forms where they may look like a work between drawing and painting; and drawing has become a more established art form with more categories, online platforms, digital art softwares and creative works in recent history.
Beside online platforms, I've found the term drawing artist used in some art books about drawing:
From Drawing by Daniel Marcus Mendelowitz (1967):
To illustrate the extent to which color has served the drawing artist, sixteen of the 314 master drawings in this book have been reproduced in full color.
From Drawing media & techniques by Joseph A. Gatto (1987):
The endless combinations of media and surfaces make it virtually impossible to explore the complete spectrum. Yet non-traditional media are not entirely different from traditional drawing media. Both offer broad artistic challenges, fresh with each drawing you begin. Both should be experienced to enable you to achieve your greatest potential as a drawing artist.
From Contemporary Drawing: Key Concepts and Techniques by Margaret Davidson (2011):
The first concept discussed in the chapters that follow is the drawing artist's deliberate choice of surface. What the surface is determines the nature of the mark. Furthermore, a focus on both the surface and the mark and the relationship between the two is one of hallmarks of contemporary drawing, and one of the most fundamental abstract issues drawing artists deal with.
Note: The author uses the term throughout the book and calls herself a drawing artist also.
Solution 2:
Drawer
Oxford dictionary definition 3
A person who produces a drawing or design.
Examples
‘The fact that these three are expert drawers and painters doesn't hurt either.’
‘The drawer's signature will be executed just above it.’
‘Jordy had always been a good drawer, he could draw trees amazingly.’
‘You've spoken about being a drawer, painter, writer too, as well as composer.’
Solution 3:
Well I am no expert and late to this question - so if it has been offered and I missed it sorry - but I call one who draws a sketch artists or a sketcher. Works for me as drawer is to easily confused and breaks the stream of consciousness for the reader when used in context of one who draws. This answer may be a little sketchy ;>.
Solution 4:
The OP in a comment said
Before stating that "drawer" IS the best possible term, try saying to yourself - as though in an introduction including your hobby - "I am a drawer". Then I think you'll see the problem. For one thing, simply saying that you're an "artist" is an uncomfortably pretentious declaration. Being termed "artist" is what others are to say ABOUT a person. The person doesn't usually say it of himself. And IN WHAT ART they participate? Bernstein, Picasso, Fellini, and Michael Jackson were ALL "artists".
First, it's obvious, according to dictionaries, that drawer IS the right word. I agree it sounds strange to my ears, but that doesn't make it incorrect. For some reason it doesn't seem to be in common usage. So let's start using it, & correct this oversight.
Second, there's nothing pretentious about calling yourself an artist if you are one, any more than calling yourself a musician, an athlete, a writer, or a politician is pretentious. If you feel self-conscious about calling yourself an artist, either gain some self-esteem to be comfortable about who you are & what you do, or change careers/hobbies.