To build on Angelin's solution, if your data contains nulls, you'll want to add IFNULL to each column:
select sum(
ifnull(char_length(column1), 0) +
ifnull(char_length(column2), 0) +
ifnull(char_length(column3), 0) +
ifnull(char_length(column4), 0) ... <-- repeat for all columns
)
from your_table