Spurs supporters chanted "We'll sing what we want" and "Yid Army" at White Hart Lane, in north London.
Before the match, the Met Police warned fans using the term could be arrested. One fan was arrested at half-time.
Spurs have a strong Jewish following and have been the target of abuse from opposition fans.
However, some Spurs supporters use the term themselves in an act of defiance.
Before the game, which West Ham won 3-0, match commander Ch Supt Mick Johnson said "racism and offensive language have no place in football".
A police spokesman said officers were speaking with fans on their way into the stadium about the issue.
The Met Police said one Tottenham fan had been arrested for a public order offence and was in custody at a north London police station.
The Football Association has warned supporters the use of such words could result in a banning order or criminal charges.
Last month, the chairman of the footballers' union, Clarke Carlisle, said fans should be banned for using the word, but Prime Minister David Cameron has said people should not be prosecuted unless it is used as an insult.
On Friday, the Tottenham Hotspur Supporters' Trust said they believed no Spurs fan "uses the term 'yid' in an offensive or insulting way".
However, it said the distinction between the use of the term as a "badge of honour and a call to arms" and the "anti-Semitic abuse levelled at our fans by supporters of opposing teams, appears to have been dismissed by the FA and the Metropolitan Police".
Before the game, West Ham United also warned supporters that "unacceptable conduct" at the match could lead to fans being banned from attending games.