I have been active on WPSE from the past week and gained 200+ rep this week until now. It does show here: Weekly Reps but not here: Weekly Reputation League
Can I assume this as a bug or being a new user I am not able to get into the reputation league?
The reputation leagues only track those with 200+ reputation and you only reached that point today (yesterday you had a rep of 198 so you just missed out). You should see yourself in the league tomorrow after it updates.
The site wide reputation leagues only update once a day unlike the weekly reps page which is part of the local site and is closer to real time.
