In just six words, the speaker makes a promise: to "write a picture." It's a small sentence with a puzzle inside it. Pictures are usually drawn, painted or photographed, so asking words to do that job feels both simple and a little impossible. The speaker seems to be announcing an intention, or maybe a challenge to themselves, to make something visible out of language.
The feeling here is quiet determination, with a touch of playfulness. "I will" is firm and confident, but the poem's short lines slow everything down, so the promise comes out one careful step at a time. Notice how the break after "a" makes us pause before the picture arrives. The mood is calm, spare and open. Because the poem doesn't tell us what the picture shows, we're left with a blank space to fill in ourselves. In a way, the poem is the first stroke, and the reader's imagination finishes the image.