It's not offensive in the UK, but it might be offensive in the US/Canada. My Canadian friend was surprised and mildly offended when I used the word 'Oriental' (we are both of Chinese descent) and she said it sounded "so old fashioned...like a word for describing a rug e.g. oriental rug"
In the US, they tend to call Chinese, Japanese, Korean etc "Asian", whereas they call people who look brow "Indian".
In the UK, "Asian" usually refers to brown people and one might say "Oriental" to refer to yellow people