Traditionally it is analyzed as a relative pronoun (a subclass of noun). However, it is now considered a subordinator.
Traditional grammar analyses the that which introduces relative clauses as a relative pronoun, comparable to which and who, but we believe that there is a good case for identifying it with the subordinator that which introduces declarative content clauses (Huddleston & Pullum, 2002: 1056).
This classification is based on four reasons, one of which is the lack of upward percolation. "Which", for example, allows a preposition to be fronted; this is called 'upward percolation' : eg. "This is the knife [with which I cut it]".
With the subordinator "that", this is clearly impossible; hence, the ungrammaticality of *"This is the knife [with that I cut it].
Note also that relative pronouns "which" and "who" inflect for the genitive case ("whose"), and the subordinator "that" does not.