Darren Tosh launched the tirade of abuse at Zuzanna Winianska after the couple broke up last year.
A sheriff told Tosh, 36, of North Erskine Street, Dundee: "You are an outrage and society casts you out. These messages are the most disgusting slur that could be put to someone."
Dundee Sheriff Court heard that after Tosh, an electrician, and Ms Winianska broke up, they remained on friendly terms as she wanted to get money back that Tosh owed her.
However, when she asked him to pay up, he sent the text messages, in which he also said she "looked like an East German shot putter".