A 37-year-old man from Exeter has been charged under the Malicious Communications Act 1988.
He has been bailed to appear before Exeter magistrates.
Mr Bradshaw has been the MP for the county town of Devon for 19 years.
When news of the attack on Mrs Cox broke he tweeted: “Absolutely ghastly news about my lovely colleague Jo Cox. Thoughts & prayers for her & her loved ones.”