Many Sepharadim have a custom to take a slight bow when saying Barechu both during Shacharit and Arvit. Others insist on standing. Is there any source for such a minhag in the sifrei Halacha (or elsewhere)? Do Ashkenazim have a similar custom?
Biur Halacha 113 (hakoreah) says it is based on Divrei haYamim I 29:20:
וַיֹּאמֶר דָּוִיד לְכָל-הַקָּהָל, בָּרְכוּ-נָא אֶת-יְהוָה אֱלֹהֵיכֶם; וַיְבָרְכוּ כָל-הַקָּהָל, לַיהוָה אֱלֹהֵי אֲבֹתֵיהֶם, וַיִּקְּדוּ וַיִּשְׁתַּחֲווּ לַיהוָה, וְלַמֶּלֶךְ.
And David said to all the congregation: 'Now bless the LORD your God.' And all the congregation blessed the LORD, the God of their fathers, and bowed down their heads, and prostrated themselves before the LORD, and before the king.
I recall that because it is questionable, the bow should be slight, not like an avos/hoda'ah bow. I cannot recall the place i saw it.
Ashkenazim practice this widely by the barchu's preceding birchos krias shema (as well as the make-up barchu's). Strangely, I don't see it widely practiced by the barch's at torah reading, though there is no reason to distinguish.
Actually, Or Letzion is against it (although some question if this is really the opinion of Rav BenTzion Abba Shaul, see comments), and Yalkut Yosef (57:9 O"H) writes that those that do it have sources to rely on. I believe this custom has a source in the Ben Ish Hai though. HaRav Musafi Shelit"a (Q&A 3176) says because we can only bow where the Hachamim decreed to do so.