I have been to every orc stronghold and can't seem to find a way to become blood kin. Their respect is not given freely.
According to the Elder Scrolls Wikia, you must complete any of these quests/challenges:
Retrieve a Daedra Heart for the Orc blacksmith Moth gro-Bagol in Understone Keep in Markarth.
Speak to the Orc miner Gat gro-Shargakh after completing the quest "Clear Kolskeggr Mine".
Retrieve The Last Scabbard of Akrash for Ghorza gra-Bagol, the Orc blacksmith stationed at the blacksmith forge near The Hag's Cure in Markarth.
Complete a series of fetch quests for Urag gro-Shub, an Orc mage and the librarian of The Arcanaeum at The College of Winterhold.
Speak to the Orc miner Lash gra-Dushnikh after killing the Silver-Blood mercenaries at Karthwasten for Ainethach. He will be nearby.
Kill a dragon near the gates of a stronghold.
Talk to Durak after completing "A New Order", from the Dawnguard questline.
After reaching level 10 and reaching Largashbur, you should find Orcs fighting a giant. Help them and you will get a questline and entrance for Largashbur. Complete the questline and you will be considered Blood-Kin.
Alternatively, being an Orc also gains you entrance into the strongholds.