JavaScript (ES6), 22 bytes

Returns a Boolean value.

s=>/^(.*)\1+$/.test(s) 

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Without a regular expression, 33 bytes

Returns a Boolean value.

s=>!!~(s+s).slice(1,-1).search(s) 

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JavaScript (ES6), 22 bytes

Returns a Boolean value.

s=>/^(.*)\1+$/.test(s) 

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Without a regular expression,  33  29 bytes

Returns either null (falsy) or an object (truthy).

s=>(s+s).slice(1,-1).match(s) 

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NB: Technically, \$s\$ is converted to a regular expression for match(), so the above title is a lie.

JavaScript (ES6), 22 bytes

Returns a Boolean value.

s=>/^(.*)\1+$/.test(s) 

Try it online!

JavaScript (ES6), 22 bytes

Returns a Boolean value.

s=>/^(.*)\1+$/.test(s) 

Try it online!

Without a regular expression, 33 bytes

Returns a Boolean value.

s=>!!~(s+s).slice(1,-1).search(s) 

Try it online!