Nope. To quote from Wikipedia:
The rules of football were codified in England by the Football Association in 1863, and the name association football was coined to distinguish the game from the other versions of football played at the time. The word soccer is a colloquial abbreviation of association (from assoc.) and first appeared in the 1880s. The word is sometimes credited to Charles Wreford Brown, an Oxford University student said to have been fond of shortened forms such as brekkers for breakfast and rugger for rugby football.
But let's assume soccer has the strongest historical claim to being called 'football'. Personally, I don't think it's appropriate to call ANY sport 'football', simply due to the confusion it can cause nowadays, regardless of any historical claim. I hate it when Americans call their sport 'football'. I hate it when Victorians call Aussie Rules 'football'. I hate it when my fellow New Zealanders call rugby union 'football'. It's unclear, imprecise, and can easily cause confusion. That's why I always stick to more precise names such as soccer. Everyone knows what sport is meant by 'soccer'.