Learn Romanian: Masajul este foarte liniștitor.

It comes from the noun liniște (peace or quiet). From that, we get the verb a liniști (to calm someone down). Adding the suffix -itor to a verb creates an adjective that describes something doing that action, making liniștitor mean soothing or calming.

Why does the neuter noun masaj take the article -ul here?

In Romanian, neuter nouns act exactly like masculine nouns when they are singular. Because masaj ends in a consonant, it takes the standard masculine definite article -ul to become masajul.

If I wanted to describe something feminine as soothing, would liniștitor change?

Yes. Like most adjectives, it must agree with the gender and number of the noun it describes. For a feminine singular noun, adjectives ending in -itor change to -itoare. For example, a soothing voice would be o voce liniștitoare.