There is precedent for
In the month of August in the year two thousand eighteen.
Some attested examples (all from the 1800s):
In the month of January in the year eighteen hundred and ninety-seven the mayor shall appoint one person to be a member of the board of health...
(An Act to Revise the Charter of the City of Holyoke)
Personally appeared before me, B. B. Breedin, a justice of the peace in and for Mobile county Curtis Lewis, for a long time one of the custom-house officers for the district of Mobile, to me well known, who, being duly sworn on the Holy Evangelists of Almighty God, did solemnly swear that he went into the service of Benjamin S. Smoot and Dennison Darling, who were sutlers in copartnership for the second regiment of United States' infantry, in the month of February, in the year eighteen hundred and thirteen. (source)
...deposeth and saith, that in the month of June, in the Year One Thousand Eight Hundred and Eleven, he was engaged to the Hudson's Bay Company for three years. (source)
...or if it be found necessary, such One or more consecutive Days, in the Month of July in the Year One thousand eight hundred and forty-one, as the said Lord Lieutenant or other Chief Governor or Governors ahall fix, severally visit every House within such Districts as may be assigned to them respectively... (source)
In many examples, instead of just the word year, we have year of our Lord, as in
...in and for the county of Jefferson, in the month of August, in the year of our Lord, one thousand eight hundred and seven, whereat the said George Tod sat as judge in a certain cause... (source)
Sometimes it's year of grace
Forget that I ever bored you with my rights and my wrongs, and I'll tell you exactly what befel me not six months ago; that is to say, in the month of August in the year of grace one thousand eight hundred and fifty-two. (source)
Finally, and less commonly, we sometimes have of the year:
After the town of Pontorson was taken again by the earl of Warwick in the manner related above, in the month of May of the year one thousand four hundred and twenty-nine... (source)