I looking for cheap lens for astrophotography with my unmodified Canon EOS 6D.

Hi,

do you want to get a new or a used one?

I had also heard good things about that lens, got myself a used one and it was a total fail 
if you get a used one, test it before you buy it 

+ here some food for thought:
Canon EF 70-300mm f/4-5.6 IS II USM

Example:
https://www.astrobin.com/am5c8g/

I started with a DSLR/Lens option. I went with a used EF300mm f4l I purchased from an Ebay vendor in Japan for about $600. I'm happy with the lens and feel like it was a good option to do both astro and daytime photography. That being said, after 7 months, I wish I had purchased a similar focal length refractor instead. I would probably go with something like this that falls within your budget.   https://www.highpointscientific.com/telescopes/refracting-telescopes/apertura-60m-fpl-53-doublet-apo-refracting-telescope-60edr

You will need the t-adapter which is about $20. And from what I know, consider a field flattener. 

If you are committed to a lens, I would avoid zoom. You can actually find a 200mm f2.8l for around your budget if you are willing to do used.

Would agree with the others, the Samyang 135 seems to be best for your budget. A lot of astrophotographers keep one of these lenses in the back pocket, for good reason. I'm still hoping to get one eventually. 

Something that could perhaps work is a cheap APO scope. Like a TS Optic 60/360 photoline
(although you might be pushing your budget as you'd need a flattener and also pushing the limits of the Star adventurer due to weight)

Since you already own a 135mm lens by the looks of it, I'd maybe look into the TPO 180 Ultrawide?  It is $400, so towards the top of that budget, but it includes its own field flattener/reducer, is light weight and shouldn't need any more adapters outside of a T-ring for your camera.  It will also have no problem working with your full frame camera as well.  The front is also threaded to take 2-inch filters, which could be of use if you need a light pollution filter.  At a focal length of 180mm (with reducer/flattener on), it may not have the reach you are going for, but it is a nice triplet design, which is ideal for astrophotography.

https://optcorp.com/products/tpo-ultra-wide-180-astrophotography-lens?variant=32007173898309

I love mine, you could also look at the Askar FMA 180, They are the same scope.

And if you take the jump into a larger mount and telescope setup, the TPO (Or Askar) can work as a good guide scope as well.