Well, Rutgers does have a Spring admission, but I don't know if they actually take people in the spring. Also, might be domestic only. http://www.physics.rutgers.edu/grad/#DESCR
. From website:
"In order to receive full consideration for financial aid, applicants should submit all materials (application, transcripts, and letters of recommendation) before January 1 for fall admission and before November 1 for spring admission."
I don't really know how to rank schools once you get outside the top 5 or 10 (mostly because my knoweldge is all on the astro side, so I don't know enough about comparing physics departments). US News and World Reports says that Rutgers physics department is 26 in the nation, so I imagine they are top 50. I would imagine there are more schools in the top 50 that do if Rutgers in fact does.
In a related note, admissionprof said somewhere that schools may not fill all positions they want, so they may have a few spots available. Maybe try asking around, especially to schools that leave the door open to applications into July (Rutgers and Texas A&M are two schools that I know of that say that).