My father in law is Romanian, and we’d like to get a visa for him to visit us in the US, but it’s not easy for Romanians to get US travel visas. It’s not impossible, but the rejection rate is fairly high compared to say Germans for whom it’s largely a formality.
Is there something I can do as a US citizen to improve his chances of getting a visa?
It is not a formality to get a visa for Germans. It is not even an issue in the same way because German nationals don’t need a visa (up to 90 days I think). They can show up, and any refusal to admit a German into the US is a separate issue.
Romania is a Road Map Country, which I take it to mean: they still need a visa, but perhaps may not need one someday soon. I’m not sure what conditions are delaying it.
Having relatives in the US can sometimes make it harder to get a visitor’s visa. It increases the chances of the visitor attempting to overstay their visit. The only situation in which you could help your dad is if he were trying to immigrate to the US.
Some visa types require that you prove you have no possible motive to spend much time in the U.S.A. Other visa types require that you prove you have no possible motive to return to your home country. This was inconvenient for me and my wife, who wanted to be able to migrate annually like birds! 
Her immigration status eventually lapsed; I wasted several hours in line at Immigration to finally be handed nothing but a huge of stack of forms to fill in. I suppose they gave me every form they had – let me figure out which were needed – but that made the hours of wait seem wasteful.
And this was all before the 11th of September…
Romania IIRC is one of the special cases because there are a lot of ethnic Romany that claim (right or wrong) persecution and try to claim refugee status, or disappear once theyreach a western country. Add to that the general influx of immigrants, legal and not, from that area seeking better economic circumstances - that is why a visa is needed.
From what little I’ve heard/read, the convincing factors would include having a life to go back to. If he has a decent job, income, house and other property, family, etc. back home, it’s more likely proof he is only coming for a short visit.
Citizens of countries in the Visa waiver agreement nowadays have to pay to apply to the US government for permission to travel to the US:
It costs about $14, and is usually instantaneous. But you can’t travel to the US without doing it.
A friend of mine, a South African citizen, had parents who emigrated to the US. (He was already an adult at the time.) He wanted to visit them, but his tourist visa application was denied because, so they said, with his parents in the US he had more connections there than here and was considered a high risk for overstaying. (I believe he appealed and did eventually get the visa.)