"vow that" is a perfectly acceptable phrase in written English.
It is commonly used to make a promise or solemn declaration about something. For example: "I vow that I will remain loyal to my partner."
The two renewed a vow that Muci made in the concentration camp.
I didn't take a Trappist vow that said that I'm never going to say anything again," he said.
"It was an unconditional vow that became conditional as the hangover set in".
It is a pledge of no backsliding - a sort of vow that never again will they thump their spouses.
"On the vow that was given to the people of Scotland, we will judge the Scotland Bill on its contents.
And vow that you've a belly-ache.
The House speaker, Nancy Pelosi, continues to vow that health legislation will pass this year.
But Hamas continues to vow that it will not recognise Israel.
The judge was skeptical about Mr. Hopwood's vow that he would change.
He declined to vow that he would stay in the race for the U.S. Senate.
Health care executives vow that in three years they'll perform CAT scans at Kinko's.
