According to Rashi Yitzchak was 37 at the time of the akeida. If that is the case why did Avraham have to arrange for Eliezer to find a wife for Yitzchak? Why couldn't Yitzchak find a wife himself?
This is my own idea here.
Avraham didn't want his son to marry one of the accursed Canaanite girls. As seen later, Yitzchak didn't want Yaakov to marry one of them either, so he presumably agreed.
Rashi to Bereishit 26:2 says that Hashem told Yitzchak not to go to Egypt because he had been prepared as a korban, and so חוץ לארץ - outside of the Land - was not good enough for him.
Perhaps Avraham also saw this, and so he didn't want Yitzchak to leave the Land and go to Charan himself, and so he sent Eliezer to find him a wife.
Alternately, as i mentioned in a comment, the custom of the time (and for a long time after) was that parents arranged their childrens' marriage.
Following though on @rikitikitembo comment on the answer 0f @scimonster asking why Avraham did this but Yitzchak did not.
Avraham was the leader of his clan and as such it was his responsibility to follow through with Yitzchak. Just as he followed Hashem's command to bring Yitzchak to the Akeidah, he realized that, just as Yitzchak had been placed in his hands for be raised to the level of kedushah (which also prevented him from leaving Eretz Yisrael), so too was he responsible now for following through on providing the wife that would be worthy of the bracha and inheritence. Note Avrohom lived until Yaakov and Eisev were 15 (another 35 years after the marriage of Yitzchak). He actually raised Rivkah (especially according to the commentary that she was three years old at the time).
Yitzchak could not go himself and (apparently) did not have an Eliezer to send. Note that he sent Yaakov specifically to Lavan to marry into the family. Also note the meforshin on Leah having "tender" eyes. It had already been arranged that Eisav was supposed to marry Leah and Yaakov was supposed to marry Rachel. In fact, this arrangement may have been set up by Avraham as well.
Had Esav fulfilled his father's expectationsa that is being Yaakov's partner, like Yissachar and Zevulun, that would ha been the course of events. Because Eisav had "turned bad", Yaakov obtained both parts of the the inheritence, the physical (Leah) and the spiritual (Rachel).
According to this shiur this was done to show that marrying into the Avrahamic family was like marrying into royalty. A royal family wouldn't send the prince to find his own wife. Furthermore, it is argued in the shiur, that doing so provides some 'space' such that if the girl would turn down the offer Yitzchak wouldn't be embarrassed.