From a previous question, around 40% of the northern hemisphere is land. Would there be a plane splitting the earth into two equal parts, where in one part there are more land than ocean?
The total land area of earth is approximately 29%. So, in order to have a hemisphere with more land than water, out of 29% of total land area we need to have at least 25% of it concentrated in that hemisphere.
Now for the ease of understanding, what does 25/29 of total land area means? It approximates to 86% of the total continental surface area.
Area of percentage
Asia (including the Middle East)- 30.0%
Africa - 20.3%
North America - 16.3%
South America - 12.0%
Antarctica - 8.9%
Europe - 6.7%
Australia (plus Oceania) - 5.2%
Now on analyzing this, it's possible to conclude you won't be able to get such a hemisphere using a plane along the longitudes.
If you try to create a hemisphere using a plane that cuts through 60˚S and 60˚N latitudes, you might be able to have most the major land together areas except Antartica and Australia and some parts of Africa in it. Still, it won't be enough to have more than half of that hemisphere with land covering it.
So, my conclusion is it's not possible to come up with such a hemisphere. :)
I wrote a little Matlab script to estimate this approximatively. Here is the result: colour denotes the total land area inside the hemisphere centred on a particular surface point. The red point is the maximum.
This gives me a maximum for the hemisphere centred on 1.7582°W longitude and 40.7692°N latitude, roughly in Guadalajara, Spain. If I calculated right this is 81% of all land, with 23.37% land area on the hemisphere (and 5.83% on the other hemisphere). So the answer to the question is no, there is no hemisphere with more land than ocean. There isn't even one with more than half land.
(Updated 2019-06-23 with higher resolution estimation, which moved the point south a bit.)