The short answer is no. And it doesn't matter how we define inflation. In Austrian economics, inflation is an increase in the money supply. Obviously higher oil prices can't cause an increase in the money supply.
The definition of inflation used commonly today refers to an increase in the general price level. While there can be a correlation between higher oil prices and price inflation, oil prices do not cause a general increase in the price level.
Higher oil prices can cause certain prices to go up. One obvious example is gasoline. Even though consumers ultimately determine prices, higher oil prices do increase the cost of gasoline, which is generally passed on to the consumer. Higher oil prices could cause other certain things to rise. If a certain item costs a lot to be shipped, perhaps the increase in transportation costs could affect the price of the item.
But we are talking about a general rise in prices. If anything, higher oil prices would have the opposite effect. Let's say that you have a family budget of $2,000 per month. Part of that budget is gasoline and you have $100 per month budgeted just for that. Now let's say that gas prices double. Most of your driving is necessary (commuting, going to the store) and you can't cut down on it. Therefore, you now have to budget $200 per month. This means you will have to cut $100 from somewhere else. Perhaps it would be eating out at restaurants or some other form of entertainment. No matter what, you will be spending $100 per month less on something else and this will actually drive other prices down.
The only way for you not to cut spending somewhere else is for your budget to increase. For this to happen, you need an increase in the amount of money you have.
Now take this example and translate it to the entire economy. If oil (and hence gasoline) prices go up, most Americans will cut somewhere else, thus driving other prices down. The only way that all or most prices can go up with oil and gas is if you have more money in the system to bid up prices. Therefore, we would need monetary inflation to drive up the overall general price level along with the price of oil. This is ignoring the short-term effects in changes of velocity or the speed at which money changes hands.
Therefore, if oil prices go up without an increase in the money supply, it is likely that some other prices will fall. This is a classic case of why the definition of inflation has changed over time. If inflation was defined as an increase in the money supply, then everyone would know to blame the Fed for higher prices. Instead, when inflation is defined as higher prices, we get to hear hacks blame everyone but the Fed and government. They will blame China, greedy businessmen, or whoever else is convenient at the time. Of course, they will also blame higher oil prices, which is obviously ridiculous based on what is written above.
Oil prices do not cause inflation. Inflation (an increase in the money supply) causes higher oil prices. Other things can cause higher oil prices like supply and demand or the perception of a coming change in the supply and demand. If we see higher oil prices and a general rise in other prices, we can be sure to blame the money creators at the Federal Reserve.