Yes, Italian has a passive infinitive for transitive verbs. As the other forms of passive voice (sono amato, saresti amato), it is formed with the auxiliary verb essere. The present passive infinitive of amare is essere amato; the past passive infinitive is essere stato amato.
As Denis remarks in a comment, one must not confuse the passive voice (voce or diatesi in Italian) of a verb with other constructions that involve a passive meaning, such as si passivante (as in In Italia si ama la pastasciutta), the mentioned da amarsi (which means “that has to be loved”), and other ones.
Verbix is not a reliable source, but the page linked doesn't even mention any passive infinitive: it lists in a haphazard way some verbal forms, without distinguishing, for instance, the present and past forms of the (active) infinitive. Websites as this one are often built automatically and mostly useless. Please consult reliable sources, such as those by Treccani or Zanichelli and, even better, an actual grammar book.