To get Pokérus, you can defeat or catch a wild pokémon who has it. To get Pokérus by fighting, it is not enough to just encounter a wild pokémon who has Pokérus and then run away; you have to actually defeat it. Unfortunately, there is no way to know if the wild pokémon has Pokérus. You just have to get lucky.
According to Bulbapedia, encountering Pokérus is even more rare than shiny pokémon. You have a 0.004069% chance of encountering Pokérus. In other words, one out of every 24,567 pokémon, statistically speaking, has Pokérus.
So no, you can't force a Pokemon to have it unless it affected by a wild Pokemon or other Pokemon affected.