Yes, you can, but it requires Pokebank, but
>Due to server expenses, use of the software requires the payment of an annual fee. This fee is ¥500 in Japan, $4.99 in the United States and Canada, £4.49 in the United Kingdom, €4.99 in Europe, $6.50 in Australia, $8.50 in New Zealand, ₩5000 in South Korea, $150 in Taiwan, $40 in Hong Kong and R$ 8.99 in Brazil. An Internet connection is required to download and use the service.
-Bulbapedia
Once you have Pokemon Bank downloaded, you can get Poke Transporter, which allows you to move Pokemon from any Gen 5 game to Pokemon Bank. To move Pokemon from a Gen 5 game, follow the instructions below
>In your copy of Pokemon Black, White, Black 2, or White 2 game, move your Pokemon to the first PC storage box and save the game.
Open up Poke Transporter and transfer all Pokemon in the first box over to the Pokemon Bank's transfer box.
Open up Pokemon Bank and transfer the Pokemon from the transfer box to one of the other boxes. This can be done one at a time or by selecting multiple Pokemon by clicking the SELECT button before choosing Pokemon with the A button.
Empty the transfer box of all Pokemon before you repeat the process.
When you want to move your Pokemon from Pokemon Bank to a Gen 6 game, select the Pokemon Link option from the main menu of the game.
Hope this helps!
Source
(Sorry if I have gotten any parts of the question incorrect, I have never used Pokemon Bank myself.)
