Is it normal that I don't have the new icon after I played Rakan with Xayah on my team twice?

"The icons will be granted within two weeks after the promotion ends."

http://na.leagueoflegends.com/en/news/champions-skins/champion-release/xayah-and-rakan-available-now-launch-promotions

The icons will be granted within two weeks after the promotion ends.

http://na.leagueoflegends.com/en/news/champions-skins/champion-release/xayah-and-rakan-available-now-launch-promotions

So yes, it might take a couple days to a couple of weeks to get the icons. Hope that helps!