In a short term, if your video collection is small, you can rent a server (VPS), prices can be as low as 1 euro a month (Arubacloud runs VPS (20G hard drive, 1G SAM, 1T traffic) to more premium ones.
You then use an FTP software to link your computer to the server, creating a folder, and store the vids on there.  Though I must say it is quite a waste to use VPS as only an online storage.  One can use VPS to do a lot of things, for example, I live in China, and I use VPS to bypass network censorship and blocking. One also can set up and host one's blog on the VPS. And in torrent's case, set up an online 24/7 seeding machine on the VPS (like a mini seedbox).  Just one week after setting up the seedbox, my ratio on GT has rocketed quite a bit, and now I never have to worry about low ratio dilemma.
In the long run, you have to buy a hard disk. It is not that expensive. I mean I am from China, and if I can afford 2 2TB disks, someone from Israel surely can as well, being a country richer than China.

FYI, utorrent has an android app (https://www.utorrent.com/mobile/) which I assume also allows you to create your own torrent file. It is very easy, you just need to follow the guide. You also need to follow the guide on this site on how to create a GT specific torrent, which requires a GT tracker (in the upload guide page). It sounds cumbersome, but it is actually quite straightforward, though as straightforward as a mobile device can be.