Here's the steps I used to change the first sample below into the second sample (not sure if it's the exact effect you're looking for, but I think it's a decent sounding basic reverse reverb.)
1.
Take your normal audio voice sample and load it into Audacity and select all.
2.
Effect --> Reverse
3.
Select the end of the sample. Generate --> Silence (one-two seconds only, I prefer one but try experimenting.)
4.
Select all. Effect --> GVerb. Set the options as follows:
Roomsize: 10.0~
Reverb Time: 1.5~
Damping: 0.15~
Input Bandwidth: Default
Dry Signal Level: 0.0 (Highest it goes)
Early reflection level: -25 to 30 dB
Tail level: 17.5 dB
5. Select all. Effect --> Amplify. It should select the appropriate amount automatically.
6. Finally, select all. Effect --> Reverse. Sample should have a nice reverse reverb on it! Hope this helps.