A solo student pilot MAY be given a special VFR clearance, however they still need to have 3SM inflight visibility, so it kind of becomes a moot point... UNLESS they need the SVFR due to cloud bases. (Such as very low overcast).
Simply put, there's no prohibition on a Student Pilot asking for or accepting/being given an SVFR, however all of the applicable rules apply, including 61.89(a)(6):
§ 61.89 General limitations.
(a) A student pilot may not act as pilot in command of an aircraft:
(1) That is carrying a passenger;
(2) That is carrying property for compensation or hire;
(3) For compensation or hire;
(4) In furtherance of a business;
(5) On an international flight, except that a student pilot may make solo training flights from Haines, Gustavus, or Juneau, Alaska, to White Horse, Yukon, Canada, and return over the province of British Columbia;
(6) With a flight or surface visibility of less than 3 statute miles during daylight hours or 5 statute miles at night;
(7) When the flight cannot be made with visual reference to the surface; or
(8) In a manner contrary to any limitations placed in the pilot's logbook by an authorized instructor.