Tests in cells suggest the drug targets some of the proteins that accumulate in this type of dementia.
The Cleveland team also analysed a database of 7m patients and found men who were on the drug had a lower risk of Alzheimer's.
More studies on it are worthwhile, they say in the journal Nature Aging.
Work like this is exciting, say experts, because repurposing an existing drug could be quicker, simpler and cheaper than finding and developing a brand new treatment.
Viagra, also known as sildenafil, was originally designed as a heart drug because of its main action - improving blood flow by relaxing or widening blood vessels.
Doctors then discovered it was having a similar effect elsewhere in the body, including the arteries of the penis, and it was developed into a successful treatment for erectile dysfunction.
But experts think it could have other uses too. Sildenafil is already used in men and women for a lung condition called pulmonary hypertension.
And scientists have recently been exploring whether it might help people at risk of vascular dementia - the second most common form of dementia after Alzheimer's - which occurs when reduced blood flow damages the brain.
Now researchers believe it may help Alzheimer's as well.
The exact cause of this type of dementia is not fully understood, but doctors do know that abnormal protein deposits collect in the brains of people who have it.
The Cleveland team found:
* High doses of the drug (larger than a person would normally take) increased brain cell growth and reduced protein accumulation in lab studies of human tissue
* People on sildenafil were less likely to develop Alzheimer's than those not taking this medication, based on personal medical data spanning six years and involving more than 7.23m individuals
Lead investigator Dr Feixiong Cheng said the findings were encouraging, but needed more exploring: "Because our findings only establish an association between sildenafil use and reduced incidence of Alzheimer's disease, we are now planning a mechanistic trial and a phase II randomized clinical trial to test causality and confirm sildenafil's clinical benefits for Alzheimer's patients."
UK brain research expert Prof Tara Spires-Jones, from the University of Edinburgh, said: "More work will be needed to know whether this drug can indeed lower risk for Alzheimer's disease.
"While these data are interesting scientifically, based on this study, I would not rush out to start taking sildenafil as a prevention for Alzheimer's disease."
Dr Jack Auty, lecturer in the Medical Sciences at the University of Tasmania, said: "In the field of Alzheimer's disease research, we have been excited by many drugs over the years, only to have our hopes dashed in clinical trials. I will be following this research group and the research around sildenafil closely."