Is it possible to get monster spawners in minecraft

Yes but only with cheats

If you use the cheat /give (playername) (itemid) (amount)

You can then use https://minecraft.gamepedia.com/ to find the item ID of the item you want. (sorry if this site goes down I don't know of any other way to find the item ID without going into the code)

For spawners the code is "52:" then a number defining what type of mob the spawner spawns.

Item IDs for all spawners

52:50 = Creeper  
52:51 = Skeleton  
52:52 = Spider  
52:53 = Giant  
52:54 = Zombie  
52:55 = Slime  
52:56 = Ghast  
52:57 = PigZombie  
52:58 = Enderman  
52:59 = CaveSpider  
52:60 = Silverfish  
52:61 = Blaze  
52:62 = Lavaslime (magma cube)  
52:63 = EnderDragon  
52:64 = WitherBoss  
52:65 = Bat  
52:66 = Witch  
52:90 = Pig  
52:91 = Sheep  
52:92 = Cow  
52:93 = Chicken  
52:94 = Squid  
52:95 = Wolf  
52:96 = MushroomCow  
52:97 = SnowMan  
52:98 = Ozelot  
52:99 = VillagerGolem  
52:100 = Horse

Try using the command /give @s mob_spawner. This will only work if your world has cheats enabled; there's no other way to get a mob spawner in your inventory. (Using a tool enchanted with silk touch doesn't work, for example.)

The mob spawner will have a pig in it by default, but you can right click the block with a spawn egg (which you can find in the "Miscellaneous" section of the creative inventory) to change the mob that spawns in it.