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The phrase "a rate that has" is correct and usable in written English.
It can be used when discussing a specific rate that possesses certain characteristics or conditions.
Example: "The report analyzed a rate that has significantly increased over the past year."
Alternatives: "a rate possessing" or "a rate exhibiting".
Exact(49)
Homebuilders are building new homes at a rate that has surprised even economists.
MICROPROCESSORS get faster every year, at a rate that has become boringly predictable.
(In US corporations, CEOs can expect to be paid 400 times an average worker's salary – a rate that has increased 20-fold since 1965).
"But sales are declining at a rate that has to be fixed, and they determined this was not the way to go".
In Saudi Arabia, the government has executed more than 80 prisoners this year alone – a rate that has it on course to double its executions total for 2015.
More than half of all households have no toilet facilities, according to the latest census figures, a rate that has worsened in the last decade.
Similar(7)
So it exchanged D-marks for Ostmarks at a rate that had no basis in economic reality.
Oh, and all the statues and paintings in the house started weeping olive oil at a rate that had the Filippo Berio factory in Italy seriously worried.
What followed in the next few days and weeks was an industrial infusion of sorts, the landing of men and machines at a rate that had never been imagined before.
The rate of preterm births in the United States was 12.8% in 2006, a rate that had increased by more than 20% between 1990 and 2006 [ 2].
That could be a problem, but it's not a rating that has changed much in recent years.
More suggestions(17)
a proportion that has
a rating that has
a frequency that has
a price that has
a pace that has
a ratio that has
a speed that has
a velocity that has
a rate that applies
a level that has
a rate that works
a rate that leaves
a rate that approximately
a rate that benefits
a statement that has
a problem that has
a joke that has
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com