In its 4.55+ billion year history the sun has orbitted the galactic centre a fair few times. It’s not unreasonable to think that it might have collected a few chunks of rock ejected by another star. If we were to find one, how could we identify it?
You need to look no further than your own body.
Complete, unsubstantiated, IANAstronomer WAG:
We know that each star has a slightly different elemental makeup. You can look at their light and see spectral lines for this or that element, and some are more ‘metal-rich’ than others. It might follow that during the mysterious dust-swirling that is planetary formation, a given star’s satellites might pick up a typical elemental (or isotopic?) composition, too.
If we did a proper survey of the bodies in various parts of our solar system – main-belt asteroids, Kuiper-belt objects, etc. etc, we’d find out what they tend to be made of, and whether there’s a system to it. And if we then found an object in an unusual orbit – say, highly elliptical and out of the ecliptic or retrograde in motion, which had an elemental composition that was a serious statistical outlier from the other bodies in the solar system, we might be able to conclude it was an import.
Then we just need to go check underneath it for the ‘Made in Alpha Leonis’ sticker. 
But actually, comets are in pretty weird orbits and are probably transformed in their composition a bit by offgassing and such when they whizz by the sun, so they might really confuse matters. And maybe the variation within the population of Sol-system bodies is greater than the difference from star to star in asteroid compositions. And maybe this WAG is way off-base alogether.
It’ll be big, red, extraordinarily heavy, and will zap anyone who touches it.
Sorry. I just finished reading Preston and Childs’ The Ice Limit last week.
Isotopic abundance would tell the tale.
Rocks and such condensed from the pre-solar nebula all have a fixed ratio, within limits, of say [sup]17[/sup]O to [sup]16[/sup]O, or [sup]13[/sup]C to [sup]12[/sup]C. Together these ratios form a sort of fingerprint identifying a rock as having formed in our very own stellar nursery. Rocks from other star forming regions have different isotope ratios.
Here’s the story of the identification of a tiny piece of silicate that came from somewhere else.
Now that’s very cool.
panache45, I assume that’s a joke, but it’s beyond me.
“I am made from the dust of the stars
And the oceans flow in my veins”
- Rush
Many of the elements that make up our bodies (and other species, I suppose) are created inside supernovae, if I recall correctly. So, by definition, parts of ourselves came from other stars than the one around which we blithely orbit.
Only if you have sweaty palms, since the discharge is triggered by salty water.
(I sometimes hate myself for the low quality of my entertainment reading.)
Things you pick up by reading old Britannica articles:
Cosmically, i.e., what’s found in the spectra of interstellar gas and other stars, the two isotopes Argon-36 and -38 comprise all but a tiny trace of the argon present in them. Our own atmosphere, however, is nearly 1% argon (0.93% by volume, IIRC), all but a trace of which is argon-40 formed by the breakdown of potassium-40. I would suspect this might be a very valuable tracer, as gas is often trapped in the formation of minerals.
No, I was serious. We are all made of stardust.
If stars were alive, we’d use a different term for the end product of their metabolism.