Can we take subway from Beijing airport to Tiananmen Square?

Yes, but you need transfer. Take the airport express to Dongzhimen, transfer to subway line 2 to Jianguomen, and take line 1 you’ll reach Tiananmen.

Personally speaking, you can take the airport shuttle bus line 2 to its terminal at Xidan and then walk to east for around 20 minutes to Tiananmen Square.