I am not a native English as you probably could understand but I think a question mark isnt too necessary. I think it can be:
can you please let me know when you arrive ?
and
can you please let me know when you will arrive ?
So like İ said the translation would be:
Bana ne zaman varacağını bildirir misin ?
(or actually bildirebilir misin because of the ´can´ )
Other wise I think Sam would have written:
Can you please let me know when you´ve arrived ? (But melike the action of arriving has finished at this sentence, but in my translation it hasn´t finished even it hasn´t started. Vardığın zaman means also varacağın zaman (in this context) in Turkish. Think Turkish way, you will understand me. But also there is difference between "Varacağın zaman bana bildir." and "Varacağın zamanı bana bildir" Varacağın zaman, bana bildir means "Let me now when you will arrive." Varacağın zamanı bana bildir means "Let me know what time(when) you will arrive." I need a question mark here i can´t know which one is which without it.