PhD in the US for Spring 2023.

I did my undergraduate at an Anna University affiliated college with a CGPA of 8.57. I am currently pursuing my MSc in Aerospace Engineering at the University of Manchester. I will be completing my masters this September and want to pursue my PhD in the US during the Winter/Spring intake. I will be applying to some universities by August. Is it worth applying for PhD for Spring intake or should I wait for Fall 2023? I have a GRE score of 316 and will get an excemption from language tests.