If Link attempts to read Lulu's Diary or Mikau's Diary while in his human form, Tatl will point out that he can't read Zoran Script. While in his Zora form, however, Link gains the physical abilities of a Zora, including the ability to read their writing. A similar phenomenon occurs when Link tries to read the unfamiliar inscriptions on Darmani's grave, but he can decipher the language by taking his Goron form.
Link only encounters Zoran Script during the events of Majora's Mask, which might mean that only Terminan Zora use it. The fact that Link had never seen the Goron writing form either before entering Termina supports that possibility.