There is no such keyboard shortcut. Hitting F8 four times will select the paragraph, but you are correct that this is not the same. Triple-clicking (left-click) selects a paragraph.
You could save the following macro in your Normal template and assign a keyboard shortcut to it if you wanted.
Code:
Sub SelectCurrentParagraph()
' Select current paragraph
'
Selection.Paragraphs(1).Range.Select
End Sub
See
Installing Macros for help using this code.