Rikke will tell you that she has a good feeling about you, but she'll still give you a test to see if you're worthy of joining the Legion. Tullius will remember you from Helgen at the start of the game, and he'll direct you to Legate Rikke, who should be nearby.
To trigger this quest, you'll first need to talk to General Tullius in Castle Dour in Solitude, and tell him that you'd like to join the Imperial Legion.
