"will invite you" is a correct and usable phrase in written English.
It is typically used as part of an invitation. For example, "We will invite you to our dinner party on Friday night."
Invite Friends to Hang Out: Popular people are always going places with their friends and if you invite people to do things with you they will invite you to do things with them (hello party invitations).
Well, perhaps Theo will invite you next time he's over.
I am sure we will invite you on other occasions".
"We will invite you to go to the bar".
We will invite you to a peaceful Mogadishu after we have chased away the enemy".
"I'm surprised how fast complete strangers will invite you into their houses," she says.
"Because people will invite you out all the time to discuss business".
You go up to villagers and they will invite you inside their home for the joy of meeting you".
These people will invite you into their homes, a "ger," or yurt as we often call them.
After the performance, the five puppeteers will invite you backstage to tell you how it all works.
He will invite you over the executive mansion for lunch and dinner and then he will invite you over to the state capitol and give you a personal tour," said Maurice Jones, Virginia Secretary of Commerce and Trade.
