Wiktionary
vb. (context transitive idiomatic English) To accept something without seeing evidence supporting it, by trust or confidence.
Usage examples of "take on faith".
The existence of mountains, deserts, and oceans he had to take on faith, like the heavenly world the nuns taught me about in catechism.
His world had always included a number of things he'd had to take on faith.
Never one to take on faith anything he was told, he had sent out his own patrols the night before, and they had confirmed that there were no Midland insurgents anywhere near Aydindril.
It seems that werewolves and dwarves have got together to do something with the Scone of Stone that would cause chaos, war, and death -- which is pretty much what you'd expect in a land where they take on faith the idea that werewolves and vampires will behave themselves on the condition that garlic isn't grown and silver isn't mined.
What couldn't be verified and what the investigators had to take on faith was that Tess and Craig weren't able to provide information that could help identify the assassins.
This you will have to take on faith, for I have no way to prove it here.