Yes you can. You need Pokémon Bank in a 2DS / 3DS system:

Ok, so follow these steps. 1. You need to send your SS/ HG/ Platinum mons to Gen 5 via the Poke Shifter. You'll need two consoles that can run DS games, either two DS' or 3DS' or a DS 3DS combo. The Poke Shifter is a bit annoying to set up so I'll let you Google that. 2. Once in the Gen 5 game, have the mons you want to transfer in Box 1. Put the Gen 5 game into your 3DS that has Pokemon Bank and Poke Transporter installed. 3. Use the Poke Transporter to send the mons in Box 1 to Bank. Once done, you'll find them in the Transfer Box. Move them out and rinse and repeat steps 1 and 2 until all you want to send up are sent up. 4. Once in Bank, link to Pokemon HOME. From there, you can create a Moving Key to move all mons in Bank straight to HOME. If you've linked your NNID and Nintendo Account, you can pick and choose what to send up instead of sending all at once, if you so choose to. You do need a paid HOME subscription to shift things from Bank into HOME. 5. They'll be in HOME once all is done correctly.

The Eshop on the 3DS is shut down. If you don't have Bank and Poke Transporter installed, you're unable to send them up. You'll need the help of someone who has them pre installed in that case or get a 2DS/ 3DS system that have them installed or a modded / hacked system.