Can someone get married on the day of fathers yorzeit?
Yes. For one who has not yet had children, the prohibition to get married is only during the 7 days of shiva. Otherwise the prohibition is for the the ‘shloshim’ the first 30 days of aveilus. After that, including the yortzeit, it is permissible to get married.
see Shulchan Aruch, Yoreh Deah, 392:1,2