Translation:I will draw a picture.
I'd say both are correct, depending on what nuance you want to give.
Strictly syntactically speaking, を would be the particle to use, since it indicates the direct object of the verb (in this case, what you draw or what you don't draw). But は is not a syntactic particle; it does not indicate what function the element does (in relation to the rest of the elements of the sentence), but it just makes the element the topic about which the sentence speaks, independently of it being the subject, an object or any complement of the verb, so it can go with any of them
With the examples that you mention: えはかきます would also be technically correct, but here you would be stressing that the topic of the sentence is the drawing (probably implying that what you draw is a drawing and not something else).
I hope that was helpful. If anyone sees something incorrect in my comment, please correct me. I am not too advanced in my Japanese studies yet
The exercise mentioned by MarilynPro6 is at https://forum.duolingo.com/comment/23002349.
My Japanese isn't particularly advanced either, but I'm fairly certain that the reason "は" is used instead of "を" in that case is because the sentence is negative. In other words, the verb meaning "to draw" isn't actually acting on the pictures because the speaker is stating that they don't draw pictures.