I recommend we don't adopt this program of rotating the earth. It's almost certainly worse than just inventing fission power and pumping desalinated sea water to wherever we want to de-desertify. We'd probably also be better off if we wasted quintillions of dollaeuroyuans on a program to terraform Mars that ends in complete failure and the deaths of millions of workers over a century, but that's also an outcome I recommend we avoid.
There are lots of countries closer to the equator - they are wetter.. large body masses have continental clima, which enocourages the growth of dessert, but they usually do so only when the war of forrest vs savannah is lost by the forrest. Which can cling to areas quiet defiantly, for example the last big forrests in syria, that once covered the middle east
Does not have to mean close to the equator.
Moist tropical air barely reaches the very top of Australia - instead it hits places like Java, where the abundant rainfall and numerous active volcanoes provide ridiculously fertile land that currently supports 150 million people - 5x that of Australia - despite being 50 times smaller.