The first to accept Islam with Rasulullah was Ali.
Tarikh al-Tabari, Vol. 6, Page 80
Zayd b. Arqam:

The first to accept Islam with the Messenger of God was 'Ali b. Abi Talib. I mentioned this to al-Nakha'i, and he denied it, saying "Abu Bakr was the first to accept Islam."

Book  : Tarikh at-Tabari
Author  : Muhammad ibn Jarir al-Tabari (224 AH - 310 AH)
English reference  : Vol. 6, Page 80
Arabic reference  : 
Narrated by: Ibn al-Muthanna, from Muhammad b. Ja'far, from Shu'bah, from 'Amr b. Murrah, from Abu Hamzah, from Zayd b. Arqam.

Note: Ibrahim al-Nakha'i never met the Prophet, yet Zayd ibn Arqam was an early Muslim, a senior leader among the Khazraj and the first to give his home for the first congregational Salaat in Islam that was led by the Prophet.