Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Americans pronounce draw as DRAH (/drɔ/). In "draw", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. This is called the DR Sounds Like JR, and it's why Americans sound more relaxed than the textbook. It comes out as DRAH. You'll hear it in sentences like "Draw a small circle" or "She saw her daughter draw a tall building" — more examples below.
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1 syllable, 3 sounds. Explore each sound's mouth shape and how it's made.
Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Relax your lips and drop your jaw significantly. The tongue tip lightly touches behind the bottom front teeth and the back part of the tongue presses down a little to create more dark space in the back of the mouth.

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The textbook way isn't wrong — it's just not how anyone actually says it.
In "draw", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. /d/ shifts toward /dʒ/ ("j"), so DR sounds like "jr".