This is really something on which you should give your own opinion. Your own opinion is much more valuable to you, and will be something that you can back up more effectively, than my opinion. Let us look at the major arguments for each side of this argument.
The conservative side of this argument holds that the War on Poverty was a failure. It argues that the war did very little to reduce poverty. As you can see in Chart 1 of this link, the official rate of poverty has not really changed since 1967, which was three years after the War on Poverty began. Furthermore, you can see in that chart that poverty was declining rapidly before the war was declared and that it stopped declining soon after the war started. This would tend to imply that the War on Poverty has failed. In addition, conservatives argue that the war has been wasteful. They say that too much has been spent on welfare programs given that those programs have not done much to reduce poverty.
Liberals argue that the War on Poverty was a success. They argue that the official poverty rate is a bad statistic that does not really capture how well people are doing. The official poverty rate only looks at income that people have before taxes. It also ignores government programs that help the poor. So, for example, the value of the food stamps that a person gets is not included in their income even though the food stamps help to improve their standard of living. That makes them look much worse off than they really are. Liberals, as in this article, argue that when you include government assistance in people’s incomes, there really is much less poverty than there used to be. If you scroll down to Chart 6 in the liberal article in the link in this paragraph, you will see a chart that purports to show how the true poverty rate (one that includes government aid as part of income) has changed since the War on Poverty and how the rate would have changed if the War on Poverty programs did not exist. It concludes that the poverty rate would be something like 13 percentage points higher if the War on Poverty had not happened. In this view, then, the War on Poverty was a big success.
The issue mostly comes down to how you think poverty should be measured. Should someone be counted as poor if their income is below the poverty line but they get enough “welfare” payments to put them over the line? If you think such people should be counted as poor, then the poverty rate has not changed much and the War on Poverty was probably a failure. However, if you think government aid should be counted in people’s incomes because it helps to improve their standard of living, you should probably conclude that the War was a success. What is your opinion?