Looks like with your visa you should be able to obtain a Social Security number. The following is excerpted from SSA's Program Operations Manual :
Aliens who submit evidence of lawful permanent resident LPR status are issued unrestricted SSN cards (without a legend) provided the evidence requirements for an SSN are met.
Under the alternate evidence of LPR status policy described in RM 10211.025C.4.a, in this section, if an I-766 card is submitted, on the face of the I-766 card the Category shown must be one of the following (status indicated in parenthesis):
* A3, A03 or A-3 (REFUGEE),
* A6, A06 or A-6 (FIANCEE – K1/CHILD – K2)
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