Assalaamu alaykum, Sheikh. I would like to know if it is haram in Islam to kill or to eat a rooster?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger. 

If the question is about the ruling on slaughtering the rooster and eating its meat, then this is permissible, because the rooster is a bird and, in principle, all birds are permissible to eat except if there is a text that forbids eating a given kind of it.

Ibn 'Abbaas, may Allah be pleased with him, narrated that the Prophet forbade eating every predator that has canine teeth and every bird that has talons. [Muslim]

Shaykh Ibn 'Uthaymeen, may Allah have mercy on him, said in Sharh Buloogh Al-Maraam, "The determining factor is what the Prophet explained: every bird that has a claw but does not hunt with it is lawful; the pigeon has a claw, the chicken has a claw, and most birds have claws, but they do not catch a prey (hunt) with it; it is for this reason that they are lawful. If we doubt about any kind of bird, then in principle, it is lawful to eat."

Shaykh Ibn 'Uthaymeen, may Allah have mercy on him, was asked, "Is it permissible to slaughter a white cock, or is it forbidden in Islam, because it is said, 'If the cock crows, it praises Allah and says, remember Allah, O you who are heedless'?" 

He replied, "The white, as well as the non-white, cock is among the animals that Allah has made lawful (to eat), so it is permissible to slaughter it, and there is nothing wrong with that. As for the fact that it praises Allah when it crows, then this is something which all other animals and birds also do, as Allah says (what means): {And there is not a thing except that it exalts [Allah] by His praise, but you do not understand their [way of] exalting.} [Quran 17:44]"

Allah knows best.