lord of the rings - Did Aragorn ever visit the Shire?

He didn't enter the Shire after becoming King (from Appendix A):

There were fourteen Chieftains, before the fifteenth and last was born, Aragorn II, who became again King of born Gondor and Arnor. ‘Our King, we call him; and when he comes north to his house in Annúminas restored and stays for a while by Lake Evendim, then everyone in the Shire is glad. But he does not enter this land and binds himself by the law that he has made, that none of the Big People shall pass its borders.

c.3000 [Saruman's] spies report that the Shire is being closely guarded by the Rangers.

3027 King Elessar issues an edict that Men are not to enter the Shire, and he makes it a Free Land under the protection of the Northern Sceptre.

3036 King Elessar rides north, and dwells for a while by Lake Evendim. He comes to the Brandywine Bridge, and there greets his friends.

As to whether he entered the Shire while he and the Dunedain were guarding it, it's not specifically mentioned. It seems likely that he probably crossed the border at some point during the years of guarding, but they most likely avoided doing it frequently given there appears to be no knowledge in the Shire of their guarding.