Can you pick up a monster spawner with silk touch?

It is not possible to get a spawner in survival, not even with a silk touch pickaxe.

One time a creeper blew up a monster spawner and it actually dropped and I was able to pick it up. I have not been able to reproduce this, though it may be possible in your version, we use different versions. I suggest testing this in creative mode in a test world.

More on Monster Spawners

If you have cheats available to you, then you can use the /setblock command, or the /clone command to either make one, or to clone the one that you already have. It looks like you probably do not have cheats available to you in this case.