How to rotate an image(player) to the mouse direction?

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You have to compute the angle of the vector from the player to the mouse. get the mouse position by pygame.mouse.get_pos() and the rectangle (pygame.Rect) around the player:

mx, my = pygame.mouse.get_pos()
player_rect = Player_1.get_rect(topleft=(P_X,P_Y))

Calculate the vector from the player to the mouse and compute the angle of vector by math.atan2. The y-axis needs to be reversed (-dy) as the y-axis is generally pointing up, but in the PyGame coordinate system the y-axis is pointing down.

dx, dy = mx - player_rect.centerx, player_rect.centery - my
angle = math.degrees(math.atan2(-dy, dx)) - correction_angle

In addition, a correction angle must be deducted (- correction_angle). The correction angle depends on the Sprite. If the Sprite

is looking to the right, the correction angle is 0: correction_angle = 0
is looking up, the correction angle is 90: correction_angle = 90
is looking to the left, the correction angle is 180: correction_angle = 180
is looking down, the correction angle is 270: correction_angle = 270

Rotate the player with pygame.transform.rotate() by the angle around its center:
(See also How do I rotate an image around its center using Pygame?)

rot_image = pygame.transform.rotate(Player_1, angle)
rot_image_rect = rot_image.get_rect(center=player_rect.center)

Minimal example: repl.it/@Rabbid76/PyGame-RotateWithMouse

import math
import pygame

pygame.init()
window = pygame.display.set_mode((300, 300))
player = pygame.image.load("player.png").convert_alpha()

#   0 - image is looking to the right
#  90 - image is looking up
# 180 - image is looking to the left
# 270 - image is looking down
correction_angle = 90

run = True
while run:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

    player_pos  = window.get_rect().center
    player_rect = player.get_rect(center = player_pos)

    mx, my = pygame.mouse.get_pos()
    dx, dy = mx - player_rect.centerx, my - player_rect.centery
    angle = math.degrees(math.atan2(-dy, dx)) - correction_angle

    rot_image      = pygame.transform.rotate(player, angle)
    rot_image_rect = rot_image.get_rect(center = player_rect.center)

    window.fill((255, 255, 255))
    window.blit(rot_image, rot_image_rect.topleft)
    pygame.display.flip()

pygame.quit()
exit()

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