WMHs are small dead areas of the brain that occur when brain cells are deprived of oxygen.
Inidvidually, they are barely detectable, but over time they are thought to contribute to mental decline.
Uric acid is known to trigger gout, a condition that is characterized by recurring attacks of joint inflammation (arthritis), deposits of hard lumps of uric acid in and around the joints and decreased kidney function and kidney stones.
The prevailing picture of men with gout is that they are overweight and middle-aged, and have high blood pressure, type 2 (or adult-onset) diabetes and often drink too much. Consequently perhaps they are also more likely to have heart attacks.
A Johns Hopkins University team analysed MRI scans of 85 men and 92 women between 20 and 92 years of age.
Those with moderately elevated levels of uric acid had an average of 2.6 times the volume of WHM than those with average or low uric acid.
Further analysis found that among the over-60s people with elevated uric acid levels had up to five times the volume of WMH.
Previous research by the same team has also shown that elevated uric acid levels were linked to poor performance on memory and speed of thought tests.
Lead researcher Dr David Schretlen said: "Having found that uric acid levels are linked to both mild cognitive decline and mini strokes we need to learn how these are related.
"We have to find out which of these factors steers the boat."
Their findings are published in the journal Neurology.
Dr Isabel Lee, of the Stroke Association, said: "Whilst this study increases our knowledge of the link between uric acid levels and strokes as well as vascular dementia it does not change clinical practice.
"This study is small and much more research needs to be done before this can happen."