I was curious as to whether there was a feat or trait for gaining a class feature for a class without having that class. Like a feat giving you bloodrage at some level-4
There is not.
Don’t really know what else to say here; I can’t prove a negative. But as a generic, “pick anything” feat, no, there is not and never will be.
Certain class features are available as feats, usually in a somewhat modified (often limited) form.
There is a way to trade a set of feats for a set of class abilities.
Many class features that can normally only be gained by taking levels in a class that grant them can be gained by the new variant multiclassing rules in Pathfinder Unchained, allowing you to trade a significant portion of your feats for certain benefits from a specific class. I don't think the Unchained Multiclassing is on the SRD yet (I didn't find it), but as examples, you can trade feats to gain Rage, Uncanny Dodge, and DR from the Barbarian class without ever taking a level in Barbarian, or several Bloodline Powers from Sorcerer. Bloodrager (and all the hybrid classes) aren't printed official options yet, as far as I'm aware.
Also, your question is clearly tagged Pathfinder, but I seem to recall an option in technically-fully-compatible (grain of salt) 3.5's Unearthed Arcana for generic classes, which had the option to take certain class features as feats. For example, the skill-focused generic class got 3/4th BAB, strong Ref save, and could take Sneak Attack and Evasion as feats, if you wanted to build a customized like-a-rogue-but-not.