UC Davis did when I got there (that was 2000 so this is very dated info). I think they gave us the option to get $1500 and then pay it off by withholding $150/month no interest. It was nice. It helped with relocation.
my program is offering a $1,500 no interest relocation loan that is paid back through payroll deduction over the first year. You should contact the specific GME director at your place and ask.
I remember when I was interviewing many moons ago that Stanford gave a $3K "signing bonus." You could almost cover first month's rent and if you were lucky, your deposit with it.
Our program allows you to borrow somewhere between 1-2k, interest free, that is then withheld from your paycheck in equal payments over your first year.