To answer your question, if by 'God', you mean a creator/omnipotent/all governing entity, the answer is No.
'God' is a Christian term. At the time of the Buddha, words like 'Mahābrahmā' or 'Brahma' were used to describe such concepts. Brahmajala sutta talks in detail about how this belief was originated.
The concept goes directly against one of the core teachings of Buddhism: "Sabbe Dhamma Anatta" - all phenomena are non-self or devoid of a soul.
Even a Jataka story questions the belief in such a being:
"If the creator of the world entire
They call God, of every being be the Lord
Why does he order such misfortune
And not create concord?"
"If the creator of the world entire
They call God, of every being be the Lord
Why prevail deceit, lies and ignorance
And he such inequity and injustice create?"
"If the creator of the world entire
They call God, of every being be the Lord
Then an evil master is he, (O Aritta)
Knowing what's right did let wrong prevail!"
Here's a related article: Buddhist attitude towards 'God'
Buddhism teaches that all misbeliefs(beliefs that block the path to Nibbana) are variations of 2 fundamental misbeliefs.
- Sassata Vada - Eternalism
- Uchcheda Vada - Nihilism
The belief of 'God' falls under the first category.
Even though holding onto such a belief does not prevent one from being born in heavens(given that they do many good deeds), it does block the path to Nibbana(Enlightenment). That's why it is called Maggavarana. Buddhism has very little to offer to such people until they are ready to give up that belief.