Unfortunately, I have to say that it is not possible to obtain a spawner in Survival mode, even if you have a tool with the Silk Touch enchantment. This means that you cannot use Silk Touch to pick up a spawner and place it elsewhere.
I know this because I have played Minecraft extensively and have come across numerous spawners in my adventures. Spawners are typically found in dungeons, mineshafts, strongholds, or other generated structures. They are encased in a cage-like structure and are responsible for spawning mobs such as zombies, skeletons, or spiders.
In creative mode, you can easily obtain a spawner by using the pick block function or by using the /give command. However, in Survival mode, spawners are not meant to be easily obtained or moved. This is likely because it would be too powerful to have the ability to create mob farms or control mob spawning locations.
Some players might think that using Silk Touch on a spawner could be a way to obtain it, as Silk Touch allows you to pick up blocks without breaking them and preserve their original form. However, Mojang, the developers of Minecraft, have specifically made spawners an exception to this rule.
So, even if you have a tool enchanted with Silk Touch, using it on a spawner will not allow you to pick it up. The spawner will simply remain in place and cannot be obtained as an item.
While Silk Touch is a valuable enchantment for obtaining various blocks in their original form, it unfortunately does not work on spawners. Spawners are meant to be a fixed part of the generated structures in Minecraft and cannot be moved or obtained in Survival mode.