It would not. An import tax reduces imports, but also reduces exports by a greater amount. An export tax on real estate transfers to foreign persons, cash or cash-equivalents, luxury goods, artwork, and technology--such as engineering documents and diagrams, manufacturing machinery, and firmware source code--would also not solve it, but it would bite a bigger chunk out of the problem.
Imports are paid for by exports. The US is currently paying for the manufacturing that it exported with dollars and documents. It could be paying with cars, and airplanes, and espresso machines, and in-sink garbage disposals, and novelty CNC lathes for engraving wooden pencils and chopsticks, and rapid refrigeration devices for single canned beverages, and maybe even non-imaginary 8K OLED television sets. If you make the specific exports that produce the most internal economic activity the cheapest way to pay for imports, increases in imports would encourage more exports.
If you're covering a trade deficit with cash, that impacts the same currency you use to conduct domestic trade--you're giving the trade partner leverage over your whole economy. What you really want to do is make a note spent in your own country buy far more than the same note spent elsewhere, so that the notes stay in the country, and the goods and services get exported instead. But you also want the rest of the world to have high demand for your currency, so that you can bring in a lot of imports, or go on lots of cheap tourist vacations. So devaluing your currency is not the best option.
But if you had, say, a 50% tax on foreign money transfers, if someone were to buy a $1 doodad from Elbonia, they would have to pay $2 for it in cash--$1 for the importer, and $1 for the tax. But they could also pay for it by purchasing a $1 doohickey locally and trading that for the $1 doodad, avoiding the tax, and keeping the $1 circulating in the domestic economy, and the Elbonian money circulating in Elbonia. Instead of taxing the trade itself, tax imbalanced trades and trade deficits.
Of course, any real-world implementation would be politicized to Hell and back, and chock full of loopholes, but it works just fine between imaginary countries.