The game, devised and developed by interactive agency Pancentric Digital and Kew, aims to celebrate the different habitats in the gardens.
It allows players to nurture and grow plants from the Alps, Desert, Rainforest and East Asia and receive rewards for their activity with new levels and prizes.
Players can choose to grow their plants via Twitter by tweeting "Kew Nutrients".
Digital media managing editor Wendy Shearer said: "This summer, we’re inviting people to see the world without leaving London by experiencing unique flora from far flung climes, from the lush rainforest to the arid desert.
"The ‘Tweet and Grow’ game gives the player a taste of this exciting world, incorporating social media elements so they can share the enjoyment with their friends and networks."