The 28-year-old player was targeted by the supposed Hammers’ fan in two foul-mouthed postings after the side lost 3-0 in south Wales.
The comments, which the player retweeted from his @CarltonCole1 account, questioned his performance and used a racist term to describe him.
An Essex Police spokeswoman said: "Police have arrested a 22-year-old man from Southend on suspicion of a racially aggravated public order offence following tweets sent to @Carltoncole1 (West Ham player Carlton Cole) on Saturday, August 25.
"Investigations are ongoing."
Following the postings Cole took to the social networking site himself to criticise his aggressor.
He said: "Listen, I take racism a lot lighter than others and I do understand the banter that comes along with it to get under people’s skin, but it can sometimes be hurtful and insulting.
"I don’t mind when people criticise me for having a bad game or they think I’m crap at football but just say that.
"Whether I am crap or had a bad game has nothing to with my race, creed or religion. lets just keep it FOOTBALL. Kapeesh?”
Fellow West Ham players Matt Jarvis, Kevin Nolan, and Guy Demel were also subjected to abuse.
Daily Telegraph football correspondent Henry Winter called for police to investigate the racist rant.
He posted on his Twitter account: "I hope the police take action over the racist abuse aimed at @CarltonCole1 on twitter tonight.”
In 2009 Cole was also the subject of racist abuse when Millwall fans at Upton Park aimed monkey chants at him during a Carling Cup clash.