In a medium saucepan, combine the chopped rhubarb and sugar. Cook over medium heat, stirring occasionally, until the rhubarb breaks down and the mixture becomes syrupy, about 10-15 minutes.
Remove the saucepan from heat and let the mixture cool slightly.
In a mixing bowl, combine the softened butter, vanilla extract, ground cinnamon, and salt. Beat with an electric mixer until creamy.
Gradually add the rhubarb mixture to the butter mixture, beating until well combined and smooth.
Transfer the rhubarb butter to a jar or airtight container and refrigerate for at least 1 hour to allow the flavors to meld.