This should handle all cases without throwing any exceptions:
--This handles dollar-signs, commas, decimal-points, and values too big or small,
-- all while safely returning an int.
DECLARE @IntString as VarChar(50) = '$1,000.'
SELECT CAST((CASE WHEN --This IsNumeric check here does most of the heavy lifting. The rest is Integer-Specific
ISNUMERIC(@IntString) = 1
--Only allow Int-related characters. This will exclude things like 'e' and other foreign currency characters.
AND @IntString NOT LIKE '%[^ $,.\-+0-9]%' ESCAPE '\'--'
--Checks that the value is not out of bounds for an Integer.
AND CAST(REPLACE(REPLACE(@IntString,'$',''),',','') as Decimal(38)) BETWEEN -2147483648 AND 2147483647
--This allows values with decimal-points for count as an Int, so long as there it is not a fractional value.
AND CAST(REPLACE(REPLACE(@IntString,'$',''),',','') as Decimal(38)) = CAST(REPLACE(REPLACE(@IntString,'$',''),',','') as Decimal(38,2))
--This will safely convert values with decimal points to casting later as an Int.
THEN CAST(REPLACE(REPLACE(@IntString,'$',''),',','') as Decimal(10))
END) as Int)[Integer]
Throw this into a Scalar UDF and call it ReturnInt().
If the value comes back as NULL, then it's not an int (so there's your IsInteger() requirement)
If you don't like typing "WHERE ReturnInt(SomeValue) IS NOT NULL", you could throw it into another scalar UDF called IsInt() to call this function and simply return "ReturnInt(SomeValue) IS NOT NULL".
The cool thing is, the UDF can serve double duty by returning the "safely" converted int value.
Just because something can be an int doesn't mean casting it as an int won't throw a huge exception. This takes care of that for you.
Also, I'd avoid the other solutions because this universal approach will handle commas, decimals, dollar signs, and checks the acceptable Int value's range while the other solutions do not - or they require multiple SET operations that prevent you from using the logic in a Scalar-Function for maximum performance.
See the examples below and test them against my code and others:
--Proves that appending "e0" or ".0e0" is NOT a good idea.
select ISNUMERIC('$1' + 'e0')--Returns: 0.
select ISNUMERIC('1,000' + 'e0')--Returns: 0.
select ISNUMERIC('1.0' + '.0e0')--Returns: 0.
--While these are numeric, they WILL break your code
-- if you try to cast them directly as int.
select ISNUMERIC('1,000')--Returns: 1.
select CAST('1,000' as Int)--Will throw exception.
select ISNUMERIC('$1')--Returns: 1.
select CAST('$1' as Int)--Will throw exception.
select ISNUMERIC('10.0')--Returns: 1.
select CAST('10.0' as Int)--Will throw exception.
select ISNUMERIC('9999999999223372036854775807')--Returns: 1. This is why I use Decimal(38) as Decimal defaults to Decimal(18).
select CAST('9999999999223372036854775807' as Int)--Will throw exception.
Update:
I read a comment here that you want to be able to parse a value like '123.' into an Integer. I have updated my code to handle this as well.
Note: This converts "1.0", but returns null on "1.9".
If you want to allow for rounding, then tweak the logic in the "THEN" clause to add Round() like so:
ROUND(CAST(REPLACE(REPLACE(@IntString,'$',''),',','') as Decimal(10)), 0)
You must also remove the "AND" that checks for "decimal-points" to allow for Rounding or Truncation.