"he arranges that" is a correct and usable phrase in written English.
You can use it when you are describing someone making plans or arrangements. For example: "He arranges that the meeting will take place on Tuesday afternoon."
He arranged that Howe's killer speech in 1990 would be heard when the chamber was full, and in complete silence, giving it maximum effect.
So he arranged that letters from both of them were read at a meeting of the Linnean Society and published in their journal.
In his mice, he arranged that the genetic element that switches on the marker gene would also prime a mechanism to make the cell self-destruct.
By the Treaty of Pressburg in 1491, he arranged that the succession to Bohemia and Hungary would pass to the Habsburgs if Vladislas left no male heir.
Enough material was amassed under his direction so that editing could begin in 1925 (publication, however, did not begin until 1931), and before his death in 1957 he arranged that it should be carried on at the University of Edinburgh.
When Mr. Barreto realized that our ravenous American teenagers kept passing on the plates of fish and making faces, he arranged that they be served chicken with rice and French fries instead.
He ordered all the corn to be brought in to his headquarters; he appointed death as the penalty for any disobedience of the order; the cattle, of which great store had been driven together by the Mandubii, he distributed man by man; he arranged that the corn should be measured out sparingly and gradually; he withdrew into the town all the force which he had posted in front of it.
He arranged that benches and tables be brought to the Wall on a daily basis for the study groups he organised and the minyan which he led there for years.
