«I’ll be oncall» — это идиома, означает следующее:
— человек по вызову,
— сидеть на телефоне и ждать звонка,
— быть наготове,
— быть вызванным в любую минуту в случае необходимости.

Т.е все, кто работает по вызову: это все срочные службы — скорая помощь, полиция, МЧС., а так же, сисдамины на удаленке, веб-специалисты, курьеры — это oncall.
В случае с моим другом из Америки, он работает в службе технической поддержки, и очень часто он работает как раз ‘on-call’.

Вот посмотрите, как он сам объясняет значение этой идиомы.

» For oncall, it means that I have to be prepared to login to my work’s network at anytime during the next 7 days.
In my case, if a bank has problems with their telephone banking product, they call the call center (centralized customer support) at my corporate headquarters, then the call center would all me and say there’s a case for me.

After they call, I need to contact the bank within a half hour. I’d login, see what the problem was, then call the bank and help them get it resolved. I do all of that from home. I might not get any calls, but I might be several. Next Monday is a holiday in the US (Presidents Day) so banks will be closed. I’ll be oncall then as well. A lot of banks do system upgrades or processing on their off days, but I shouldn’t get too many calls. We don’t get as many calls on weekends as we did in the past.» (с)

Example sentences containing ‘on call’:

A doctor on call.
On-call guy.
A typical oncall.
Any active On-Call issues.
You do love oncall duty, don’t you?
Oncall is probably enough of a punishment already.
Our biggest oncall issues were the people actually doing the calling.
In general, my last callout on an oncall day is 7:59pm PT.
As a Tier 3 network engineer I am always on call.
But at night there is usually less experience and they need to contact an on call person.

I’m basically on-call 24/7.
I was basically on call 24/7.
Being on call for a month can be difficult, but having 4 months without being on call makes it worth it to me.
Monday oncall rotation.
A weekend of rest after your on-call week!
On-call should be used for things that can NOT wait until morning.
I’ve worked in all sorts of «ON CALL» environments and at different tiers.

Ну, и как вы видите, пишут они ‘on call’ по-разному — и слитно и раздельно и через дефис.