My shul has a policy that anyone (male, over Bar Mitzva, of course) not wearing tefillin cannot receive an aliyah. Is there any halacha or minhag to support this rule?
My rav is in Eretz Yisra'el, now, so I cannot ask him directly.
A suggestion which I admit is not totally supported by the quoted source.
www.torah.org has an article on tefillin from which I abstracted some lines which might be put together to justify the policy of your shul.
In short I am thinking that the shul might think that to read from the Torah one needs a clean body (guf noki) and that someone not wearing tefillin might not have a guf noki.
The relationship between tefillin and Torah is very significant:
1 The very mention of tefillin in to be found in the context of Torah learning: "You shall teach them [the Torah] thoroughly to your children…Bind them as a sign upon your arm and let them be totafos (tefillin) between your eyes" (Devarim 6:7-8).
The tefillin house four Torah passages (Shemos 13:1-10, Shemos 13:11-16, Devarim 6:4-9 & Devarim 11:13 -21) which are written on parchment like a Torah scroll.
2 One who wears tefillin is compared to one who is reading from the Torah (Pesikta Zutrasa Shemos 13).
3 Torah in its entirety is compared to tefillin (Makkos 11a, Rosh Hashanah 17a).
And in the same way that the holiness of Torah housed in the tefillin demands the wearer to have a clean body (guf noki) to wear these religious artifacts (Shulchan Aruch, Orach Chaim 38:1-2), so too, should the holiness of Torah indeed filter down and spiritualize our physical bodies.