The almost 120-metre Starship was poised to blast off from the southern tip of Texas, near the Mexican border, on Thursday.
SpaceX's Elon Musk gave 50-50 odds of the spacecraft reaching orbit on its debut.
None of the rocket will be recovered.
Instead, if all goes well, the first-stage booster, dubbed Super Heavy, will drop into the Gulf of Mexico.
The spacecraft on top will continue eastward, passing over the Atlantic, Indian and Pacific Oceans before ditching near Hawaii.
The whole flight, if successful, will last just 90 minutes.
The company plans to use Starship to send people and cargo to the moon and, eventually, Mars.
NASA has reserved a Starship for its next moonwalking team and rich tourists are already booking lunar flybys.
A stuck booster valve scrapped Monday's first launch attempt.
Hundreds of space fans have returned to the launch site at Boca Chica Beach on the eve of the second launch attempt, snapping more selfies.
"I've been waiting for this, really, for years," said Bob Drwal, a retired engineer who drove from Chicago with wife Donna.
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