Just to add on to what ToonMariner said, that website provides both a formula and a VBA solution. I found the author's details on using the formula a bit confusing. Using the provided formula:
Simply highlight one column by clicking the header and name it 'BlanksRange'
The 'BlanksRange' column should hold your values. (Column A from your screenshot)
Highlight a second column and name it 'NoBlanksRange'.
Click the first cell in 'NoBlanksRange', paste the formula into the formula textbox at the top, and press CTRL-SHIFT-ENTER at the same time
With the first cell still highlighted, click the bottom right corner of that first cell and drag this down to the same number of rows as the 'BlanksRange' column.
Wait a few seconds (depending on the data) and your desired output will be revealed.
Make sure you wait a few seconds to see the results... on my machine, even only 10 rows or so required about 4 seconds before the correct data showed up.
Also make sure when you copy and paste the formula from a website that the whole thing gets in there because the linebreaks may cause it to only paste a portion of the formula.
If you select the column and press F5, click Special, choose Blanks then right click the selected cells and delete - that'll get rid of the empty cells.
Not my bag but I also found this.