Can anyone be a psyker? Or is it just certain classes? If others can then how can they gain the psyker talent? i.e how can a missionary or a arch militant for example become a psyker?

Check the rules for the Witch-Born Lineage option inside Into the Storm.

Alternatively, Wyrdling mutation can get you psychic powers.

Of course, both of those leave the character as an unsanctioned witch. Which is fine until they get caught.

For another option, have a look at the sorcery rules in Edge of the Abyss. Great for intelligent characters who don't mind the great risks.

couldnt find anything about sorcerer rules in that book. You sure that is the right book? Can i have a page/chapter reference?

Lord Bronicus said:

Page 84, right after the Chaos Psychic Powers.

Alternatively, some GMs might allow someone to take psyker as an Elite Advance. It doesn't seem like something that would be incredibly unbalancing to me, especially if every other psyker related talent and skill you wanted to take was also an elite advance, you'll be paying out the nose for your powers and that extra bit of versatility that you get by having a non-psyker career path.

One exception to this, I can only recall two instances of psykers being members of the Adeptus Mechanicus (Grey Knight Techmarines and Corrupted Techpriest Sorcerers making Heretechnical devices). So I wouldn't allow a techpriest to be a psyker under almost any circumstances.

See i for one can't see how the Machine Cult could not have any psykers at all, their pretty much a pocket empire who does a lot of autonomous things, surely they have some psykers. Maybe they don't have any "home grown" ones per the treaty that ties them to terra but I doubt there's anything abotu machine cult doctrine or implants that forbids psykers.

Just my two bits.

The mainstream Mechanicus hate and distrust psykers. Psychic powers make a mockery of physical law and are far too random for the liking of (most) Magi. There are a handful of Magi who experiment with psy-tech, but that's a far cry from tolerating psykers in their own ranks.

If you don't mind porting over some of the transition packages from DH: Ascension, you can offer The Mind's Eye Opens as an elite advance. Without going back to Terra, this would result in an unsanctioned psyker, but there are consequences for everything

EDIT: This would be more for a high-level game that starting characters IMHO.