The first to accept Islam with Rasulullah was Ali.
Tarikh al-Tabari, Vol. 6, Page 81
Zayd b. Arqam:

The first to accept Islam with the Messenger of God was 'Ali b. Abi Talib.

Book  : Tarikh at-Tabari
Author  : Muhammad ibn Jarir al-Tabari (224 AH - 310 AH)
English reference  : Vol. 6, Page 81
Arabic reference  : 
Narrated by: Abu Kurayb, from Waki', from Shu'bah, from 'Amr b. Murrah, from Abu Hamzah the mawla of the Ansar, from Zayd b. Arqam.